几类分布参数神经网络的稳定性及其同步
|
摘要
神经网络在模式识别、图像处理、信号处理、控制问题和保密通信等领域已经取得成功应用。分布参数时滞神经网络稳定性的研究受到了国内外学者的广泛关注。神经网络存在时滞、随机干扰和分布参数等情况下的许多理论问题仍没有系统解决。本论文以Lyapunov泛函理论、自由权矩阵、Green公式、L-算子不等式、随机分析等方法为主要手段，对分布参数时滞神经网络的动力学行为进行了系统深入研究。论文的工作主要体现在以下几个方面:
1利用自由权矩阵结合Lyapunov-Krasovskii泛函方法,研究了具有离散和分布时滞反应扩散神经网络的全局指数稳定性。通过构造Lyapunov-Krasovskii泛函，利用自由权矩阵表示牛顿–莱布尼兹公式中各项的关系,获得了系统时滞相关的全局指数稳定性判据，且该判据依赖于空间测度，与先前结果相比具有较少保守性。
2.利用自由权矩阵结合Lyapunov-Krasovskii泛函方法,探讨了一类具有混合时滞和部分转移概率未知的随机马尔科夫跳变反应扩散神经网络的稳定性。得到了用线性矩阵不等式表示的平衡点均方渐近稳定充分条件，所得结果是时滞依赖和空间依赖。
3.利用著名L-算子微分不等式、线性矩阵不等式技巧和Lyapunov-Krasovskii泛函方法,研究了具有混合时滞脉冲随机反应扩散神经网络的动态行为问题,分别获得了具有混合时滞脉冲随机反应扩散神经网络周期解的存在唯一性和均方全局指数稳定和p阶指数稳定新的判据。给出了具有时滞、脉冲和随机综合因素影响的反应扩散神经网络的稳定性的充分条件，此判据改进了已有的结果。通过仿真研究表明所得结果是有效的。
4.首次提出具有马尔科夫跳变参数和Dirichlet边界条件的反应扩散时滞神经网络的几乎输入状态稳定性的概念，通过构造Lyapunov泛函和利用不等式技巧，给出了其几乎输入状态稳定性充分条件。当输入为零时，该判断准则能保证系统的几乎全局指数稳定。实例仿真证实了本文所用的方法和得到的结果是有效的。
5.研究了一类不确定性分布参数系统的鲁棒指数稳定性和稳定化问题。利用推广到Hilbert空间的Lyapunov－Krasovskii方法和不等式技巧,给出了线性时滞系统的鲁棒指数稳定性和可稳定化的充分条件，该条件是时滞依赖，并把得到的结果应用到一个抛物型方程，得到用线性矩阵不等式表示的抛物型方程指数稳定的判据。
6．讨论了一类反应扩散时滞BAM神经网络模型。通过构造Lyapunov泛函，利用驱动-响应方法，设计了反馈控制率，得到了使驱动和响应反应扩散时滞BAM神经网络全局指数同步新的判据。这个判据用两个简单不等式表示，容易检验。
7研究了具有反应扩散项随机时滞神经网络自适应同步问题。由Lyapunov-Krasovskii泛函理论和随机分析结合的方法，利用自适应反馈控制理论，得到了用线性矩阵不等式表示两个分布参数神经网络渐近同步新的判断准则。基于LaSalle泛函微分方程不变原理，得到了具有未知时变耦合强度反应扩散时滞神经网络自适应渐近同步新的判据。所用方法发展和改进了已有结果。通过实例仿真,证实了本文所用的方法和得到的结果的可行性和有效性。
Neural networks have obtained their successful applications in many areas such aspattern recognition，image processing，control problem and secure communication etc.The problems of dynamical behaviors of neural networks with distributed parametersand time delays has long received extensive attention from researchers working insystems and intelligent control communist. However, there are few results, or even noresults concerning the dynamical behaviors issues for neural networks withreaction–diffusion or/and mixed time-varying delays or/and stochastic perturbations.Based on Lyapunov functional theory，free-weighting matrx，Green formula，L-operaterinequality and stochastic analysis etc., dynamical behaviors of neural networks withdistributed parameter are systematically and deeply investigated. The maincontributions of this dissertation are listed as follows:
1. By constructing a more general type of Lyapunov–Krasovskii functionalcombined with free-weighting matrix approach and analysis techniques,delay-dependent exponential stability criteria are derived in the form of linear matrixinequalities. The obtained results are dependent on the size of the time-varyingdelays and the measure of the space, which are usually less conservative thandelay-independent and space-independent ones.
2. The problem of dynamics analysis is proposed for a class of novel stochasticMarkovian jump reaction–diffusion neural networks with partial information ontransition probability and mixed time delays. The new criterion for the asymptoticalstability of the equilibrium point in the mean square sense is obtained based on linearmatrix inequality forms. An improved Lyapunov–Krasovskii functional andfree-connection weighting matrices are introduced to derive the condition. The obtainedresults are dependent on delays and the measure of the space.
3. The dynamical behaviors of impulsive stochastic reaction–diffusion neuralnetworks (ISRDNNs) with mixed time delays are discussed. By combining awell-known L-operator differential inequality with mixed time delays and theLyapunov-Krasovkii functional approach, as well as linear matrix inequality technique,some novel sufficient conditions are derived to ensure the existence, uniqueness andglobal exponential stability of the periodic solutions and p moment global exponentialstability for ISRDNNs with mixed time delays in the mean square sense and p momentglobal exponential stability of ISRDCGNNs, respectively. The results are new andimprove some of the previously known results. The proposed model is quite general since many factors such as noise perturbations, impulsive phenomena and mixed timedelays are considered. Numerical examples are provided to verify the usefulness of theobtained results.
4. Almost sure input-to-state stability definition is firstly proposed for the delayedreaction–diffusion neural networks with Markovian jump parameters and Dirichletboundary conditions. By constructing new Lyapunov functional and utilizing someinequality techniques, sufficient conditions ensuring the almost sure input-to-statestability are given. The criteria can also ensure almost sure global exponential stabilitywhen the input is equal to zero. Numerical example is given to demonstrate theeffectiveness of the proposed approach and derived results.
5. Robust exponential stability and stabilization conditions are presented foruncertain linear distributed parameter delayed systems. Based on extension theLyapunov-Krasovskii method to a Hilbert space and linear matrix inequality technique,robust exponential stability and stabilization criteria are given, respectively. The criteriaare dependent on time delay. Being applied to a parabolic equation, exponential stabilitycriterion for parabolic equation is reduced to standard linear matrix inequalities.
6. A delay-differential equation modelling a BAM neural networks withreaction-diffusion terms is investigated. A feedback control law is derived to achievethe state global exponential synchronization of drive and response BAM NNs withreaction-diffusion terms by constructing a suitable Lyapunov functional, using thedrive-response approach and some inequality technique. A novel global exponentialsynchronization criterion is given in terms of two identical inequalities, which can bechecked easily.
7. The adaptive synchronization problems for delayed neural networks withreaction-diffusion terms are studied. At first, an approach combining Lyapunovfunctional theory with stochastic analysis and the adaptive feedback control technique istaken to investigate this problem. Some novel sufficient conditions in terms of linearmatrix inequalities are obtained to ensure the asymptotic synchronization for theproposed drive and response neural networks. Then, based on the LaSalle invariantprinciple of functional differential equations, a sufficient condition for the adaptivesynchronization of such a system is obtained. Numerical example is given to show the feasibility and effectiveness of the proposed scheme and derived results.
1利用自由权矩阵结合Lyapunov-Krasovskii泛函方法,研究了具有离散和分布时滞反应扩散神经网络的全局指数稳定性。通过构造Lyapunov-Krasovskii泛函，利用自由权矩阵表示牛顿–莱布尼兹公式中各项的关系,获得了系统时滞相关的全局指数稳定性判据，且该判据依赖于空间测度，与先前结果相比具有较少保守性。
2.利用自由权矩阵结合Lyapunov-Krasovskii泛函方法,探讨了一类具有混合时滞和部分转移概率未知的随机马尔科夫跳变反应扩散神经网络的稳定性。得到了用线性矩阵不等式表示的平衡点均方渐近稳定充分条件，所得结果是时滞依赖和空间依赖。
3.利用著名L-算子微分不等式、线性矩阵不等式技巧和Lyapunov-Krasovskii泛函方法,研究了具有混合时滞脉冲随机反应扩散神经网络的动态行为问题,分别获得了具有混合时滞脉冲随机反应扩散神经网络周期解的存在唯一性和均方全局指数稳定和p阶指数稳定新的判据。给出了具有时滞、脉冲和随机综合因素影响的反应扩散神经网络的稳定性的充分条件，此判据改进了已有的结果。通过仿真研究表明所得结果是有效的。
4.首次提出具有马尔科夫跳变参数和Dirichlet边界条件的反应扩散时滞神经网络的几乎输入状态稳定性的概念，通过构造Lyapunov泛函和利用不等式技巧，给出了其几乎输入状态稳定性充分条件。当输入为零时，该判断准则能保证系统的几乎全局指数稳定。实例仿真证实了本文所用的方法和得到的结果是有效的。
5.研究了一类不确定性分布参数系统的鲁棒指数稳定性和稳定化问题。利用推广到Hilbert空间的Lyapunov－Krasovskii方法和不等式技巧,给出了线性时滞系统的鲁棒指数稳定性和可稳定化的充分条件，该条件是时滞依赖，并把得到的结果应用到一个抛物型方程，得到用线性矩阵不等式表示的抛物型方程指数稳定的判据。
6．讨论了一类反应扩散时滞BAM神经网络模型。通过构造Lyapunov泛函，利用驱动-响应方法，设计了反馈控制率，得到了使驱动和响应反应扩散时滞BAM神经网络全局指数同步新的判据。这个判据用两个简单不等式表示，容易检验。
7研究了具有反应扩散项随机时滞神经网络自适应同步问题。由Lyapunov-Krasovskii泛函理论和随机分析结合的方法，利用自适应反馈控制理论，得到了用线性矩阵不等式表示两个分布参数神经网络渐近同步新的判断准则。基于LaSalle泛函微分方程不变原理，得到了具有未知时变耦合强度反应扩散时滞神经网络自适应渐近同步新的判据。所用方法发展和改进了已有结果。通过实例仿真,证实了本文所用的方法和得到的结果的可行性和有效性。
Neural networks have obtained their successful applications in many areas such aspattern recognition，image processing，control problem and secure communication etc.The problems of dynamical behaviors of neural networks with distributed parametersand time delays has long received extensive attention from researchers working insystems and intelligent control communist. However, there are few results, or even noresults concerning the dynamical behaviors issues for neural networks withreaction–diffusion or/and mixed time-varying delays or/and stochastic perturbations.Based on Lyapunov functional theory，free-weighting matrx，Green formula，L-operaterinequality and stochastic analysis etc., dynamical behaviors of neural networks withdistributed parameter are systematically and deeply investigated. The maincontributions of this dissertation are listed as follows:
1. By constructing a more general type of Lyapunov–Krasovskii functionalcombined with free-weighting matrix approach and analysis techniques,delay-dependent exponential stability criteria are derived in the form of linear matrixinequalities. The obtained results are dependent on the size of the time-varyingdelays and the measure of the space, which are usually less conservative thandelay-independent and space-independent ones.
2. The problem of dynamics analysis is proposed for a class of novel stochasticMarkovian jump reaction–diffusion neural networks with partial information ontransition probability and mixed time delays. The new criterion for the asymptoticalstability of the equilibrium point in the mean square sense is obtained based on linearmatrix inequality forms. An improved Lyapunov–Krasovskii functional andfree-connection weighting matrices are introduced to derive the condition. The obtainedresults are dependent on delays and the measure of the space.
3. The dynamical behaviors of impulsive stochastic reaction–diffusion neuralnetworks (ISRDNNs) with mixed time delays are discussed. By combining awell-known L-operator differential inequality with mixed time delays and theLyapunov-Krasovkii functional approach, as well as linear matrix inequality technique,some novel sufficient conditions are derived to ensure the existence, uniqueness andglobal exponential stability of the periodic solutions and p moment global exponentialstability for ISRDNNs with mixed time delays in the mean square sense and p momentglobal exponential stability of ISRDCGNNs, respectively. The results are new andimprove some of the previously known results. The proposed model is quite general since many factors such as noise perturbations, impulsive phenomena and mixed timedelays are considered. Numerical examples are provided to verify the usefulness of theobtained results.
4. Almost sure input-to-state stability definition is firstly proposed for the delayedreaction–diffusion neural networks with Markovian jump parameters and Dirichletboundary conditions. By constructing new Lyapunov functional and utilizing someinequality techniques, sufficient conditions ensuring the almost sure input-to-statestability are given. The criteria can also ensure almost sure global exponential stabilitywhen the input is equal to zero. Numerical example is given to demonstrate theeffectiveness of the proposed approach and derived results.
5. Robust exponential stability and stabilization conditions are presented foruncertain linear distributed parameter delayed systems. Based on extension theLyapunov-Krasovskii method to a Hilbert space and linear matrix inequality technique,robust exponential stability and stabilization criteria are given, respectively. The criteriaare dependent on time delay. Being applied to a parabolic equation, exponential stabilitycriterion for parabolic equation is reduced to standard linear matrix inequalities.
6. A delay-differential equation modelling a BAM neural networks withreaction-diffusion terms is investigated. A feedback control law is derived to achievethe state global exponential synchronization of drive and response BAM NNs withreaction-diffusion terms by constructing a suitable Lyapunov functional, using thedrive-response approach and some inequality technique. A novel global exponentialsynchronization criterion is given in terms of two identical inequalities, which can bechecked easily.
7. The adaptive synchronization problems for delayed neural networks withreaction-diffusion terms are studied. At first, an approach combining Lyapunovfunctional theory with stochastic analysis and the adaptive feedback control technique istaken to investigate this problem. Some novel sufficient conditions in terms of linearmatrix inequalities are obtained to ensure the asymptotic synchronization for theproposed drive and response neural networks. Then, based on the LaSalle invariantprinciple of functional differential equations, a sufficient condition for the adaptivesynchronization of such a system is obtained. Numerical example is given to show the feasibility and effectiveness of the proposed scheme and derived results.
引文
[1]张化光.递归时滞神经网络的综合分析与动态特性研究[M].北京:科学出版社,2008.
[2]黄立宏，李雪梅.细胞神经网络动力学[M].北京:科学出版社，2007.
[3] Hebb D. O.The Organization of Behavior[M]. Wiley, New York,1949.
[4] Wu JH. Theory and application of partial functional differential equations [M]. NewYork: Springer,1996.
[5] Minsky M. Papert S. Perceptrons. MIT Press，1969.
[6] Hopfield JJ. Neural Networks and physical Systems with Emergent CollectiveComputational Abilities, Proeeedings of the National Academy of Sciences of theUnited States of America[J].[part l: Biological Sciences]1982,79(8):2554–2558.
[7] Hopfield J. J. Neurons with Graded Response Have Collective ComputationalProperties like Those of Two-State Neurons, Proeeedings of the National Academyof Sciences of the United States of America [part1:Biological Sciences][J].1984,81(10)；3088-3092.
[8] Cohen MA, Grossberg S.. Absolute Stability of Global pattern Formation andParallel Memory Storage by Competitive Neural Networks [J]. IEEE Transactionson Systems，Man and Cybernetics1983,13(5):815–826.
[9] Grossberg S. Nonlinear neural networks-principles, Mechanisms，and Architectures，Neural Networks[J].1988,1(1):17-61.
[10] Kosko B. Bidirectional Associative Memories, IEEE Transactions on Systems，Man and Cybernetics[J].1988,18(1):40–60.
[11] Chua LO., Yang L. Cellular Neural Networks: Theory，IEEE Transactions onCircuits and Systems[J].1988,35(10):1257-1272.
[12] Chua LO., Yang L. Cellular Neural Networks: Applications [J],IEEE TransactionsOn Circuits and Systems[J].1988,35(10)，1273-1290.
[13]廖晓昕，傅予力，高建，赵新泉.具有反应扩散的Hopfield神经网络的稳定性[J].电子学报，2000，28(1):78–80.
[14]廖晓昕，杨叔子，程时杰，沈轶.具有反应扩散的广义神经网络的稳定性[J].中国科学:E辑2002，32(1):87–94.
[15] Serrano-Gotarredona T, Linares-Barranco B. Log-domain implementation ofcomplex dynamics reaction-diffusion neural networks[J]. IEEE Transactions onNeural Networks,2003,14:1337–1355.
[16] Zhang WY, Li JM, Chen ML. Dynamical behaviors of impulsive stochasticreaction–diffusion neural networks with mixed time delays[J]. Abstract andApplied Analysis,2012,2012:1-21.
[17]刘永清,谢胜利.滞后分布参数系统的稳定与变结构控制[M].广州：华南理工大学出版社,1998.
[18]胡跃明，周其节.分布参数变结构控制系统[M].北京:国防工业出版社，1996.
[19]崔宝同,楼旭阳.时滞分布参数系统理论及其应用[M].北京:国防工业出版社，2009.
[20]王林山.时滞递归神经网络[M].北京:科学出版社，2008.
[21]王林山，徐道义.变时滞反应扩散Hopfield神经网络的全局指数稳定性[J].中国科学: E辑，2003,33(6):488–495.
[22] Qiu JL, Cao JD. Delay-dependent exponential stability for a class of neuralnetworks with time delays and reaction–diffusion terms [J]. Journal of theFranklin Institute,2009,346:301–314.
[23] Wang Z, Zhang H. Global Asymptotic Stability of Reaction-DiffusionCohen-Grossberg Neural Network with Continuously Distributed Delays [J].IEEE Trans Neural Netw,2010,21:39-49.
[24] Erbe L H, et al. Comparison principles for impulsive parabolic equations withapplications to models of single species growth [J]. J Austral Math Soc, Ser B,1991,32(4):382-400.
[25] Ballinger G, Liu X. Existence, uniqueness, results for impulsive delay differentialequations[J]. Dynamics of Continuous Discrete and Impulsive System,1999,5:579-591.
[26]闫宝强，傅希林.局域无限时滞的脉冲微分方程解的存在性.中国学术期刊文摘，1999,12(5).
[27] D.Bainov, Kdzislaw，E.Minehev，Monotone iterative methods for impulsivehyperbolic differential functional equations[J]. J. Comput. APPl. Math.,1996，70:329–347.
[28] Kamont Z， Turo J, Zubik-Kowl B, Differential and difference inequalitiesgenerated by mixed problems for hyperbolic functional d1fferential equationswith impulses[J]. APPl. Math Comput,1996,80:127-154.
[29]邓立虎，葛渭高.脉冲时滞抛物型方程解的振动准则[J].数学学报，2001，44(3):501–506.
[30] Qiu J. Exponential stability of impulsive neural networks with time-varying delaysand reaction-diffusion term[J]. Neurocomputing,2007,70:1102-1108.
[31] Li K. Song Q. Exponential stability of impulsive Cohen-Grossberg neural networkswith time-varying delays and reaction-diffusion term[J]. Neurocomputing,2008,1-3,(72):231-240.
[32] Li ZA, Li KL. Stability analysis of impulsive Cohen–Grossberg neural networkswith distributed delays and reaction–diffusion terms[J]. Applied MathematicalModeling,2009,33:1337–1348.
[33] Pan J, Liu XZ, Zhong SM. Stability criteria for impulsive reaction-diffusionCohen-Grossberg neural networks with time-varying delays[J]. Math. Comput.Modell.2010,51:1037-1050.
[34] Zhu W. Global exponential stability of impulsive reaction-diffusion equation withvariable delays[J]. Appl. Math. Comput.,2008,205:362-369.
[35] Pan J, Zhong SM. Dynamical behaviors of impulsive reaction-diffusionCohen-Grossberg neural network with delays[J]. Neurocomputing,2010,73:1344-1351.
[36]齐民友.线性偏微分算子引论(上册)[M].北京:科学出版社，1984.
[37]伍卓群，尹景学，王春朋.椭圆与抛物型方程引论[M].北京:科学出版社，2003.
[38]陈亚浙.二阶抛物型偏微分方程[M].北京:北京大学出版社，2003.
[39]王明新.非线性抛物型方程[M].北京:科学出版社，1997.
[40] Kallianpur G，Xiong J. Stochastic Differential Equationsin Infinite Dimensions[J].1995,26, IMS Lecture Notes, Hayward, California.
[41] Babugka I, Andersson B, Smith P J, Levin K. PartI: Statistical analysis on fiberscale[J]. Comput. Methods Appl. Mech. Engrg.1999,172:27-77.
[42] Elishakoff I, Ren Y. The bird's eye view on finite element method for structureswith large stochastic variations[J]. Comput. Methods Appl. Mech. Engrg.1999,168:51-61.
[43] Ghanem RG, Kruger R M. Numerical solution of spectral stochastic finite elementsystems[J]. Comput. Methods Appl. Mech. Engrg.,1996,129:289-303.
[44] Taniguchi T. Almost sure exponential stability for stochastic partial functionaldifferential equations[J]. Stochastic Anal. Appl.1998,16(5):965-975.
[45]罗琦，邓飞其，包俊东.一类随机分布参数系统反馈控制的镇定[J].控制理论与应用,2005,22(3):477-480.
[46]赵碧蓉邓飞其罗琦.中立型分布参数随机系统的指数稳定性[J].华南理工大学学报,2004,32(12):70-74.
[47] Park Ju H, yun H, Cho J. A delay-dependent asymptotic stability criterion ofcellular neural networks with time-varying discrete and distributed delays[J].Chaos, Solitons and Fractals,2007,33:436-442.
[48] Cao J, Wang J. Global asymptotic and robust stability of recurrent neural networkswith time delays[J]. IEEE Transactions on Circuits and Systems I: FundamentalTheory and Applications,2005,52(2):417–426.
[49]王占山.连续时间时滞递归神经网络的稳定性[M].沈阳:东北大学出版社,2007.
[50] Wu RC. Exponential convergence of BAM neural networks with time-varyingcoefficients and distributed delays[J]. Nonlinear Analysis: RWA,2010,11:562-73.
[51] Zou F, Nossek JA. Bifurcation and chaos in cellular neural networks[J]. IEEETrans Circuits and Systems I1993,40:166-173.
[52] Lu HT. Chaotic attractors in delayed neural networks [J]. Physics Letters A,2002,298:109-119.
[53] Song QK, Cao JD, Zhao ZJ. Periodic solutions and its exponential stability ofreaction–diffusion recurrent neural networks with continuously distributeddelays[J]. Nonlinear Anal., Real World Appl.2006,7:65–80.
[54] Liang JL, Cao JD. Global exponential stability of reaction–diffusion recurrentneural networks with time-varying delays[J]. Phys. Lett. A,2003,314:434–442.
[55] Song QK, Zhao ZJ, Li YM. Global exponential stability of BAM neural networkswith distributed delays and reaction–diffusion terms[J]. Phys Lett A,2005,335:213–225.
[56] Wang ZS., Zhang HG., Li P. An LMI Approach to Stability Analysis ofReaction–Diffusion Cohen–Grossberg Neural Networks Concerning DirichletBoundary Conditions and Distributed Delays[J]. IEEE Trans. Syst. Man Cybern. B,2010,40:1596-1606.
[57] Wang LS, Zhang RJ, Wang YF. Global exponential stability of reaction–diffusioncellular neural networks with S-type distributed time delays[J]. Nonlinear Analysis:RWA,2009(10):1001–1113.
[58] Zhang WY, Li JM. Global exponential stability of reaction–diffusion neuralnetworks with discrete and distributed time-varying delays[J]. Chin. Phys. B,2011,20(3):030701.
[59] Lu J. Robust global exponential stability for interval reaction-diffusion Hopfieldneural networks with distributed delays[J]. IEEE Trans Circ Syst II2007,54:1115–1119.
[60]楼旭阳,崔宝同.一类分布参数动态系统的周期性分析[J].自动化学报，2009，35(1):77-84.
[61]邓飞其，赵碧蓉，罗琦.具分布参数的随机Hopfield神经网络的指数稳定[J]，控制理论与应用,2005,22(2):196-200.
[62]罗琦，邓飞其，包俊东，赵碧蓉，傅予力.具分布参数的随机Hopfield神经网络的镇定[J].中国科学(E辑)，2004,34(6):619-628.
[63] Zhu Q, Li X., Yang XS. Exponential stability for stochastic reaction–diffusionBAM neural networks with time-varying and distributed delays[J]. Appl. Math.and Comput.2011,217:6078-6091.
[64]罗琦，邓飞其，包俊东.随机分布参数型Hopfield时滞神经网络的稳定[J].数学物理学报，2006,26A(6)：968-977.
[65]罗琦，邓飞其，毛学荣，包俊东，张雨田.随机反应扩散系统稳定性的理论与应用[J].中国科学(E辑)，2007,37(10):1272-1284.
[66] Xu X, Zhang J， Zhang W. Mean square exponential stability of stochastic neuralnetworks with reaction-diffusion terms and delay[J]. Appl. Math. Lett.2011,(24):5-11.
[67]廖晓昕.稳定性的数学理论和应用[M].武汉:华中师范大学出版社，2001.
[68]黄琳.稳定性理论[M].北京:北京大学出版社2001.
[69]钱学森，宋健.工程控制论[M].上下册科学出版社，1980，1981.
[70]廖晓昕.动力系统的稳定性理论和应用[M].北京:国防工业出版社，2000.
[71] Amraoui S, Rhali SL. Monotonicity and stability for some reaction-diffusionsystems with and Dirichlet boundary conditions [J]. J. Math. Anal. Appl.,2001,255:458-479.
[72] Ahmad S, Rao MR. Stability of Volttera diffusion equations with time delays [J].Appl. Math. Comput.,1998,90:143-154.
[73] Farkas G, Sinom PL., Stability properties of positive solutions to partial differentialequations with delay[J]. Electronic J. Diff. Equs.,2001(64):1-8.
[74] Simon H.神经网络原理[M].叶世伟，史忠植(译).北京:机械工业出版社，2004.
[75]钟守铭,刘碧森，王晓梅，范小明，神经网络稳定性理论[M].北京:科学出版社，2008.
[76] Rakkiyappan R., Balasubramaniam P. Delay-dependent asymptotic stability forstochastic delayed recurrent neural networks with time varying delays [J]. Appl.Math. Comput.2008,198:526–533.
[77] Huang CX., Cao JD. Convergence dynamics of stochastic Cohen-Grossberg neuralnetworks with unbounded distributed delays [J]. IEEE Trans. Neural Netw.,201122:561-572.
[78] Zhang C. Dynamic analysis of reaction–diffusion Cohen–Grossberg neuralnetworks with varying delays and Robin boundary conditions [J]. Chaos, Solitonsand Fractals2009,42:1724–1730.
[79] Zhang ZQ, Yang Y, Huang YS. Global exponential stability of interval generalBAM neural networks with reaction–diffusion terms and multiple time-varyingdelays [J]. Neural Networks,2011,24:457-465.
[80] Yang ZG, Xu DY. Global dynamics for non-autonomous reaction-diffusion neuralnetworks with time-varying delays [J]. Theoretical Computer Science,2008,403:3–10.
[81] Song QK, Cao JD. Global exponential robust stability of Cohen–Grossberg neuralnetworks with time-varying delays and reaction–diffusion terms [J]. Journal of theFranklin Institute2006,343:705-719.
[82] Liu PC, Qiang Y. etc. Analysis on global exponential robust stability ofreaction–diffusion neural networks with S-type distributed delays[J]. Physica D:Nonlinear Phenomena,2008,237:475–485.
[83] Wang LS, Zhang Y, Zhang Z, Wang YF. LMI-based approach for globalexponential robust stability for reaction–diffusion uncertain neural networks withtime-varying delay [J]. Chaos, Solitons and Fractals2009,41:900–905.
[84] Balasubramaniam P, Vidhya C. Global asymptotic stability of stochastic BAMneural networks with distributed delays and reaction-diffusion terms[J]. Journal ofComputational and Applied Mathematics,2010,234:3458-3466.
[85] Karimi H, Gao H. New delay-dependent exponential H∞synchronization foruncertain neural networks with mixed time delays[J]. IEEE Transactions onSystems Man, and Cybernetics-Part B: Cybernetics,2010,40:173–185.
[86] Pecora LM, Carroll TL. Synchronization in chaotic systems [J]. Physical ReviewLetters,1990,64:821-824
[87] K.Aihara, Takabe T., Toyoda M. Chaotic neural networks[J]. Physics Letters A,1990,144:333-340
[88] Balasubramaniam P, Chandran R, Jeeva Sathya Theesar S. Synchronization ofchaotic nonlinear continuous neural networks with time-varying delay[J].Cognitive Neurodynamics,2011,(5):361–371.
[89] He W, Cao JD. Adaptive synchronization of a class of chaotic neural networkswith known or unknown parameters[J]. Physics Letters A,2008,372:408–416.
[90] Milanovic V, Zaghloul M. Synchronization of chaotic neural networksandapplications to communications[J]. International Journal of Bifurcation and Chaos,1996,6:2571–2585.
[91] Hu C., Yu J., Jiang H., Teng, Z. Exponential lag synchronization for neuralnetworks with mixed delays via periodically intermittent control[J]. Chaos,2010,20:023108.
[92] Barsella A, Lepers C. Chaotic lag synchronization and pulse lasers coupled bysaturableabsorber [J]. Optics Communications,2002,205:397-403.
[93] Shahverdiev EM, Sivaprakasam S., Shore KA. Lag synchronization intime-delayed systems[J]. Physics Letters A,2002,292(6):320-324.
[94] Gilles Renversez. Synchronization in two neurons: Results for model withtime-delayedinhibition[J]. Physica D,1998,114:147-171.
[95] S. Arkady. Pikovsky, Michael G. Rosenblum, Grigory V. Osipov. Kurths, Jürgen.Phase synchronization of chaotic oscillators by external driving[J]. Physica D,1997,104:219-238.
[96] R. Mainieri, J. Rehacek. Projective synchronization in three-dimensional chaoticsystems[J]. Physical Review Letters,82(1999):3042-3045.
[97] Voss HU. Anticipating chaotic synchronization[J]. Physical Review E,2000,61(5):5115-5119.
[98] Boccaletti S, Kurths J, Osipov G, Valladares DL., Zhou CS. The synchronizationof chaotic systems[J]. Physics Reports,2002,366:1-101.
[99] Carrol TL, Pecora LM. Synchronization of chaotic circuits [J]. IEEE Trans Circuitsand Systems,1991,38:453-456.
[100] Pecora L M, Carroll T L. Cascading synchronized chaotic systems [J]. Physica D,1993,67:126-140.
[101] Wang Y, Cao JD. Synchronization of a class of delayed neural networks withreaction–diffusion terms[J]. Physics Letters A,2007,369:201–211.
[102] Zhang WY, Li JM. Global exponential synchronization of delayed BAM neuralnetworks with reaction-diffusion terms and the Neumann boundary conditions[J].Boundary Value Problems2012(2): doi:10.1186/1687-2770-2012-2.
[103] Gan QT. Global exponential synchronization of generalized stochastic neuralnetworks with mixed time delays and reaction-diffusion terms[J].Neurocomputing,2012,89:96-105.
[104] Wang K. Teng ZD. Jiang HJ. Global exponential synchronization in delayedreaction-diffusion cellular neural networks with the Dirichlet boundaryconditions[J].Math. Comput. Modell,2010,52:12-24.
[105] Lou XY, Cui BT. Asymptotic synchronization of a class of neural networks withreaction-diffusion terms and time-varying delays [J]. Computers Math. Appl.,2006,52:897-904.
[106] Wang Y, Cao JD. Synchronization of a class of delayed neural networks withreaction-diffusion terms[J]. Phys. Lett. A,2007,369:201-211.
[107] Hu C, Yu J, Jiang H, Teng Z. Exponential synchronization for reaction–diffusionnetworks with mixed delays in terms of p-norm via intermittent driving[J].Neural Networks,2012,31:1–11.
[108] Shi G, Ma Q. Synchronization of stochastic Markovian jump neural networkswith reaction-diffusion terms[J]. Neurocomputing,2012,77:275–280.
[109] Gan QT. Exponential synchronization of stochastic Cohen–Grossberg neuralnetworks with mixed time-varying delays and reaction–diffusion via periodicallyintermittent control[J]. Neural Networks,2012,31:12–21.
[110] S. Sivaprakasam, Shahverdiev EM, Spencer PS, Shore KA. ExperimentalDemonstration of Anticipating Synchronization in Chaotic Semiconductor Laserswith Optical Feedback[J]. Physical Review Letters,2001,86,15401-1-3.
[111] John JK, Amritkar RE. Synchronization of unstable orbits using adaptive control[J]. Physical Review E,1994,49:4843-4848.
[112] Sheng L, Yang H, Lou XY. Adaptive exponential synchronization of delayedneural networks with reaction-diffusion terms[J]. Chaos, Solitons and Fractals,2009,40:930-939.
[113] Yang T, Chua L. Impulsive control and synchronization of nonlinear dynamicalsystemsand application to secure communication [J]. International Journal ofBifurcation and Chaos,1997,7:645-664.
[114] Hu C, Jiang HJ, Teng ZD. Impulsive control and synchronization for delayedneural networks with reaction-diffusion terms[J]. IEEE Trans Neural Netw,2010,21:67-81.
[115] Nicaise S, Pignotti C. Stability and Instability Results of the Wave Equationwith a Delay Term in the Boundary or Internal Feedbacks[J]. SIAM Journal onControl and Optimization,2006,45(5):1561-1585.
[116] Cao JD, Wang J. Global exponential stability and periodicity of recurrent neuralnetworks with time delays[J]. IEEE Trans Circ Syst I,2005,52:920–931.
[117] Arik S, Orman Z. Global stability analysis of Cohen-Grossberg neural networkswith time-varying delays[J]. Phys. Lett. A,2005,341:410–421.
[118] Chen T, Rong L. Delay-independent stability analysis of Cohen–Grossberg neuralnetworks[J]. Phys. Lett. A,2003,317:436-449.
[119] He Y, Wu M, She J, Liu G. Delay-dependent robust stability criteria for uncertainneutral systems with mixed delays[J]. Systems and Control Letters,2004,51(1):57-65.
[120] Gu K., Kharitonov V., Chen J. Stability of Time-Delay Systems[J]. Birkhauser,Boston,2003.
[121] Liao XX, Yang SZ, Cheng SJ., Fu YL. Stability of generalized networks withreaction-diffusion terms [J]. Sci. China Ser. F,2001,44:87–94.
[122]廖晓昕,傅予力等.具有反应扩散项的Hopfield神经网络的稳定性[J].电子学报,2000,28:78～82.
[123] Lee SM，Kwon OM，Ju H. Park. A new approach to stability analysis of neuralnetworks with time-varying delay via novel Lyapunov--Krasovskii functional[J].Chin. Phys. B,2010,19(5):50507.
[124] Arena P, Fortuna L, Branciforte M. Reaction–diffusion CNN algorithmstogenerate and control artificial locomotion[J]. IEEE Transactions on Circuits andSystems I,1999,46:253–260.
[125] Ensari T, Arik S. Global stability analysis of neural networks with multiple timevarying delays[J]. IEEE Transactions on Automatic Control,2005,50(11):1781–1785.
[126] Erbe L H, et al. Comparison principles for impulsive parabolic equations withapplications to models of single species growth [J]. J Austral Math Soc, Ser B,1991,32(4):382-400.
[127] Haykin S, Neural Networks[M]. Prentice-Hall, NJ,1994.
[128] Vidhya C, Balasubramaniam P. On the stability of the stochastic parabolic Itoequation with delay and Markovian jump[J]. Computers and Mathmatics withApplications,2010,60:1959-1963.
[129] Boccaletti S, Kurths J., Osipov G., Valladares DL., Zhou CS. Thesynchronization of chaotic systems[J]. Physics Reports,2002,366:1-101.
[130] Li XD. Existence and global exponential stability of periodic solution forimpulsive Cohen–Grossberg-type BAM neural networks with continuouslydistributed delays[J]. Applied Mathematics and Computation2009,215:292–307.
[131] Hardy GH, Littlewood JE, Polya G. Inequalities, second edition[M]. CambridgeUniv. Press, London,1952.
[132] Mao XR. Stochastic Differential Equation and Application [M]. HorwoodPublishing, Chichester,1997.
[133] Li ZA, Li KL. Stability analysis of impulsive Cohen–Grossberg neural networkswith distributed delays and reaction–diffusion terms[J]. Applied MathematicalModeling,2009,33:1337–1348.
[134] Huang CX, Cao JD. On pth moment exponential stability of stochasticCohen–Grossberg neural networks with time-varying delays[J]. Neurocomputing,2010,73:986–990.
[135] Wang XH, Guo QY, Xu DY. Exponential p-stability of impulsive stochasticCohen–Grossberg neural networks with mixed delays[J]. Math. Comput. Simulat.2009,79:1698–1710.
[136] Rong LB, LMI approach for global periodicity of neural networks withtime-varying delays[J]. IEEE Trans. on Circuits and Systems I: Regular papers,2005,52(7):1451-1458.
[137]廖晓昕,昌莉,沈轶，离散Hopfield神经网络的稳定性研究.自动化学报,1999,25(6):721-727.
[138] Zhang Y, Pheng H A, Vadakkpepat P, Absolute periodicity and absolute stabilityof delayed neural networks[J]. IEEE Trans. on Circuits and System I:Fundamental Theory and Applications,2002,49(2):256-261.
[139] Cao J, Wang L. Exponential stability and Periodic oscillatory solution in BAMnetowrks with delays[J]. IEEE Trans. on Neura1Networks,2002,13(2):457-463.
[140]盛立,杨慧中,楼旭阳.具有漏泄时滞的的高阶细胞神经网络的的多周期性分析[J].控制理论与应用，2010,27(1):103-106.
[141] Civalleri P, Gilli M. Practical stability criteria for cellular neu-ral networks[J].Electronics Letters,1997,33(11):970–971.
[142] Cao JD, Feng G, Wang Y. Multistability and multiperiodicity of delayedCohen-Grossberg neural networks with a general class of activation functions[J].Physica D,2008,237(13):1734–1749.
[143] Pan J., Zhan YX. On periodic solutions to a class of non-autonomously delayedreaction-diffusion neural networks[J]. Commun Nonlinear Sci Numer Simulat2011,16:414-422.
[144] Lv Y, Lv W, Sun J. Convergence dynamics of stochastic reaction-diffusionrecurrent neural networks with continuously distributed delays[J]. NonlinearAnal. RWA.,2008(9):1590-1606.
[145] Lu J, Lu L. Global exponential stability and periodicity of reaction-diffusionrecurrent neural networks with distributed delays and Dirichlet boundaryconditions[J]. Chaos, Solitons and Fractals2009,39:1538–1549.
[146] Li X. Existence and global exponential stability of periodic solution for delayedneural networks with impulsive and stochastic effects[J]. Neurocomputing,2010,73:749-758.
[147] V. Lakshmikantham, S. Leela. Differential and Integral Inequalities[M]. NewYork: Academic,1969.
[148] Liang J, Wang Z, Liu Y, Liu X. Global synchronization control of generaldelayed discrete-time networks with stochastic coupling and disturbances[J].IEEE Trans. Syst. Man and Cybern. B Cybern,2008,38:1073-1083.
[149] Zhou QH, Wan L, Sun JH. Exponential stability of reaction–diffusion generalizedCohen–Grossberg neural networks with time-varying delays [J]. Chaos, Solitonsand Fractals2007,32:1713–1719.
[150] Luo XY, Cui BT. Boundedness and exponential stability for nonautonomouscellular neural networks with reaction–diffusion terms [J]. Chaos, Solitons andFractals2007,33:635–62.
[151] Cui BT, Luo XY. Global exponential stability of BAM neural networks withdistributed delays and reaction–diffusion terms [J]. Chaos, Solitons and Fractals,2006,27:1347–1354.
[152] Wang L, Zhang Z, Wang Y. Stochastic exponential stability of the delayedreaction–diffusion recurrent neural networks with Markovian jumpingparameters[J]. Physics Letters A,2008,372:3201–3209.
[153]肖晓波,奚宏生,季海波.不确定Markov跳跃线性系统的鲁棒跟踪与模型跟随[J].控制与决策,2006,21(12):1432–1436.
[154] Xu SY, Chen TW． H∞output feedback control for uncertain stochastic systemswith time-varying delays[J]. Automatica,2004,40(12):2091-2098．
[155] Wang ZD，Lam J，Liu XH． Exponential filtering for uncertain Markovian jumptime-delay systems with nonlinear disturb-ances[J]. IEEE Trans on Circuits andSystems Part Ⅱ，2004,51(5):262-268．
[156] Shi P，Karan M，Kaya C Y．Robust Kalman filtering design for Markovian jumplinear systems with norm-bounded un-know n nonlinearties[J]．Circuits，Systemsand Signal Processing，2005，24(2):135-150．
[157] Boukas EK，Liu ZK． Robust stability and stability of Markov jump linearuncertain systems with mode-dependent time delays[J]. Journal of OptimizationTheory and Applications，2001，109(3):587-600．
[158] Liu YR, Wang ZD, Liu XH, Exponential synchronization of complex networkswith Markovian jump and mixed delays [J]. Phys. Lett. A,2008,372(22):3986-3998.
[159] Cao Y, Lam J. Robust H∞control of uncertain Markovian jump systems withtime-delay[J]. IEEE Transactions on Automatic Control,2000,45(1):77–83.
[160] Mao X. Exponential stability of stochastic delay interval systems with Markovianswitching[J]. IEEE Transactions on Automatic Control,2002,47(10):1604–1612.
[161] Xu S, Lam J. Delay-dependent H∞control and filtering for uncertain Markovianjump systems with time-varying delays[J]. IEEE Transactions on Circuits andSystem,2007,54(9):2070–2077.
[162] Xu S, Chen T, Lam J. Robust H∞filtering for uncertain Markovian jump systemswith mode-dependent time delays[J]. IEEE Trans-actions on Automatic Control,2003,48(5):900–907.
[163] Chen WH, Cu JX, Guan ZH. Guaranteed cost control for uncer-tain Markovianjump systems with mode-dependent time-delays[J], IEEE Transactions onAutomatic Control,2003,48(12):2270–2275.
[164] Shao HY. Delay-rang-dependent robust H∞filtering for uncertainstochasticsystems with mode-dependent time delays and Markovianjump parameters[J].Journal of Mathematical Analysis and Applications,2008,342(2):1084–1095.
[165] Zhu Q, Cao JD. Stability of Markovian jump neural networks with impulsecontrol and time varying delays[J]. Nonlinear Analysis: Real World Applications2012,13:2259–2270.
[166] Wang Y, Lin P, Wang L. Exponential stability of reaction–diffusion high-orderMarkovian jump Hopfield neural networks with time-varying delays[J].Nonlinear Analysis: Real World Applications2012,13:1353–1361.
[167] Zhang LX, Boukas EK. Stability and stabilization of Markovian jump linearsystems with partly unknown transition probabilities[J]. Automatica,2009,45(2),436-468.
[168] Zhang LX,. Boukas EK, Lam J. Analysis and synthesis of Markov jump linearsystems with time-varying delays and partially known transition probabilities[J].IEEE Transactions on Automatic Control,2009,53(10):2458-2464.
[169] Zhang Y, He Y, Wu M, Zhang J. Stabilization for Markovian jump systems withpartial information on transition probability based on free-connection weightingmatrices[J], Automatica,2011,47:79-84.
[170] X. Lou, Cui B. Stochastic stability analysis for delayed neural networks of neutraltype with Markovian jump parameters[J]. Chaos, Solitons and Fractals,2009,39(5):2188-2197.
[171] Teng L, Yan P. Dynamical behaviors of reaction–diffusion fuzzy neuralnetworks with mixed delays and general boundary conditions[J]. CommunNonlinear Sci Numer Simulat,2011,16:993-1001.
[172] Li T, Luo Q, Sun CY, Zhang BY. Exponential stability of recurrent neuralnetworks with time-varying discrete and distributed delays[J]. Nonlinear Anal.:RWA,2009(10):2581–2589.
[173] Sontag ED. Smooth stabilization implies coprime factorization[J], IEEETransaetions Automatic Control,1989,34:435–443.
[174] Kokotovie P., Areak M.. Constructive nonlinear control: a historical perspective[J]. Automatica,2001,37:637–662.
[175] Sontag ED, Wang Y. On charaeterizations of the input to state stability property[J].Systems and Control Letters,1995,24:351–559.
[176] Sontag ED，Wang Y. New echaraeterizations of the input to state stabilityproperty[J], IEEE Transactionson Automatic Control，1996,41:1283–1294..[177] Sontag ED. Comments on integral variants of ISS [J]. Systems and ControlLetters1998,34:93–100.
[178] Huang L, Mao X. On input-to-state stability of stochasticretarded systems withMarkovian switching[J]. IEEE Trans Automat Control,2009,54(8):1898–1902.
[179] Fridman E, Dambrine M, Yeganefar N， On input-to-state stability of systemswith time-delay: A matrix inequalities approach[J]. Automatica,2008,44:2364–2369.
[180] Yu W, Li X, Some stability properties of dynamic neural networks[J]. IEEETrans Circuits Syst I Fundam Theory Appl,2001,48(2):256–259.
[181] Sanchez EN, Perez JP，Input-to-state stability analysis for dynamic neuralnetworks[J]. IEEE Trans Circuits Syst I FundamTheory Appl,1999,46(11):1395–1398.
[182] Guo Y. New results on input-to-state convergence for recurrent neural networkswith variable inputs[J]. Nonlinear Anal RWA.2008(9):1558–1566.
[183] Ahn CK. Passive learning and input-to-state stability of switched Hopfield neuralnetworks with time-delay[J]. Inform Sci,2010,180:4582–4594.
[184] Zhu S, Shen Y. Two algebraic criteria for input-to-state stability of recurrentneural networks with time-varying delays[J]. Neural Comput and Applic,2012,23, DOI10.1007/s00521-012-0882-9.
[185] Adimurthi. Hardy-sobolev inequality in H1and its applications[J].Commun Contemp Math,2002(4):409-434.
[186] Wang T. Stability in Abstract Functional-differential equations[J]. II Applications.Journal of Mathematical Analysis and Applications.1994,186:835-861.
[187] Fridman E, Orlov Y. Exponential Stability of Linear Distributed ParameterSystems with Time-varying Delays[J]. Automatica,2009,45:194–201.
[188] Curtain R, Zwart H. An Introduction to Infinite-dimensional Linear Systems[M].1995, Springer-Verlag.
[189] Pazy A. Semigroups of Linear Operators and Application to Partial DifferentialEquations [M], New York:Springer-Verlag,1983.
[190] R. Temam. Infinite Dimensional Dynamical Systems in Mechanics and Physics.Springer-Verlag, New York, Berlin1998.
[191] Sarasola C. Feedback synchronization of chaotic systems [J]. InternationalJournal of Bifurcation and Chaos,2003,13:177-191.
[192] Salarieh H，Shahrokhi M．Adaptive synchronization of two different chaoticsystems with time varying unknown parameters[J]．Chaos，Solitons andFractals，2008，37(1)：125-136．
[193] Sun FY, Zhao Y, Zhou TS．Identify fully uncertain parameters and designcontrollers based on synchronization[J]. Chaos, Solitons and Fractals，2007，34(5)：1677-1682．
[194] Park JH．Adaptive modified projective synchronization of a unified chaoticsystem with all uncertain parameter[J]. Chaos，Solitons and Fractals，2007，34(5)：1552-1559．
[195] LI Z，Jiao L，Lee JJ. Robust adaptive global synchronization of complexdynamical networks by adjusting time-varying coupling strength. Physica A,2008,387:1369-1380.
[196] Chen L，Wu L，Zhua S. Synchronization in complex networks by adjustingtime-varying couplings. Eur.Phys. J. D,2008,48:405-409.
[197] Huang LH， Wang ZY, Wang YN. Synchronization analysis of delayed complexnetworks via adaptive time-varying coupling strengths. Physics Letters A，2009，373:3952–3959.
[198] Guo XY, Li JM, A new synchronization algorithm for delayed complex dynamicalnetworks via adaptive control approach, Commun Nonlinear Sci Numer Simulat,2012,17(11):4395-4403.
[199] Hale JK, Theory of functional differential equation[M]. New York:Springer-Verlag,1977.
[200] Allegretto W., Papini D. Stability for delayed reaction–diffusion neural networks[J]. Physics Letters A,2007,360,669–680.
[201]叶其孝、李正元著，反应扩散方程引论[M]，科学出版社，1999年，北京.
[202] Zhang X., Wu S., Li KL. Delay-dependent exponential stability for impulsiveCohen–Grossberg neural networks with time-varying delays and reaction–diffusionterms[J]. Commun Nonlinear Sci Numer Simulat,2011,16:1524–1532.
[203] Bainov D, Kdzislaw ZZ, Minchev E. Monotone iterative methods for impulsivehyperbolic differential functional equations[J]. J. Comput. Appl. Math.,1996,70:329-347.
[204]燕居让.脉冲中立型时滞微分方程的振动性[J].数学年刊,2000,21A (6):755-762.
[205] Zhang WY, Li JM, Shi NZ. Stability analysis for stochastic Markovian jumpreaction–diffusionneural networks with partially known transition probabilitiesand mixed time delays[J]. Discrete Dynamics in Nature and Society,2012,2012:1-17.
[2]黄立宏，李雪梅.细胞神经网络动力学[M].北京:科学出版社，2007.
[3] Hebb D. O.The Organization of Behavior[M]. Wiley, New York,1949.
[4] Wu JH. Theory and application of partial functional differential equations [M]. NewYork: Springer,1996.
[5] Minsky M. Papert S. Perceptrons. MIT Press，1969.
[6] Hopfield JJ. Neural Networks and physical Systems with Emergent CollectiveComputational Abilities, Proeeedings of the National Academy of Sciences of theUnited States of America[J].[part l: Biological Sciences]1982,79(8):2554–2558.
[7] Hopfield J. J. Neurons with Graded Response Have Collective ComputationalProperties like Those of Two-State Neurons, Proeeedings of the National Academyof Sciences of the United States of America [part1:Biological Sciences][J].1984,81(10)；3088-3092.
[8] Cohen MA, Grossberg S.. Absolute Stability of Global pattern Formation andParallel Memory Storage by Competitive Neural Networks [J]. IEEE Transactionson Systems，Man and Cybernetics1983,13(5):815–826.
[9] Grossberg S. Nonlinear neural networks-principles, Mechanisms，and Architectures，Neural Networks[J].1988,1(1):17-61.
[10] Kosko B. Bidirectional Associative Memories, IEEE Transactions on Systems，Man and Cybernetics[J].1988,18(1):40–60.
[11] Chua LO., Yang L. Cellular Neural Networks: Theory，IEEE Transactions onCircuits and Systems[J].1988,35(10):1257-1272.
[12] Chua LO., Yang L. Cellular Neural Networks: Applications [J],IEEE TransactionsOn Circuits and Systems[J].1988,35(10)，1273-1290.
[13]廖晓昕，傅予力，高建，赵新泉.具有反应扩散的Hopfield神经网络的稳定性[J].电子学报，2000，28(1):78–80.
[14]廖晓昕，杨叔子，程时杰，沈轶.具有反应扩散的广义神经网络的稳定性[J].中国科学:E辑2002，32(1):87–94.
[15] Serrano-Gotarredona T, Linares-Barranco B. Log-domain implementation ofcomplex dynamics reaction-diffusion neural networks[J]. IEEE Transactions onNeural Networks,2003,14:1337–1355.
[16] Zhang WY, Li JM, Chen ML. Dynamical behaviors of impulsive stochasticreaction–diffusion neural networks with mixed time delays[J]. Abstract andApplied Analysis,2012,2012:1-21.
[17]刘永清,谢胜利.滞后分布参数系统的稳定与变结构控制[M].广州：华南理工大学出版社,1998.
[18]胡跃明，周其节.分布参数变结构控制系统[M].北京:国防工业出版社，1996.
[19]崔宝同,楼旭阳.时滞分布参数系统理论及其应用[M].北京:国防工业出版社，2009.
[20]王林山.时滞递归神经网络[M].北京:科学出版社，2008.
[21]王林山，徐道义.变时滞反应扩散Hopfield神经网络的全局指数稳定性[J].中国科学: E辑，2003,33(6):488–495.
[22] Qiu JL, Cao JD. Delay-dependent exponential stability for a class of neuralnetworks with time delays and reaction–diffusion terms [J]. Journal of theFranklin Institute,2009,346:301–314.
[23] Wang Z, Zhang H. Global Asymptotic Stability of Reaction-DiffusionCohen-Grossberg Neural Network with Continuously Distributed Delays [J].IEEE Trans Neural Netw,2010,21:39-49.
[24] Erbe L H, et al. Comparison principles for impulsive parabolic equations withapplications to models of single species growth [J]. J Austral Math Soc, Ser B,1991,32(4):382-400.
[25] Ballinger G, Liu X. Existence, uniqueness, results for impulsive delay differentialequations[J]. Dynamics of Continuous Discrete and Impulsive System,1999,5:579-591.
[26]闫宝强，傅希林.局域无限时滞的脉冲微分方程解的存在性.中国学术期刊文摘，1999,12(5).
[27] D.Bainov, Kdzislaw，E.Minehev，Monotone iterative methods for impulsivehyperbolic differential functional equations[J]. J. Comput. APPl. Math.,1996，70:329–347.
[28] Kamont Z， Turo J, Zubik-Kowl B, Differential and difference inequalitiesgenerated by mixed problems for hyperbolic functional d1fferential equationswith impulses[J]. APPl. Math Comput,1996,80:127-154.
[29]邓立虎，葛渭高.脉冲时滞抛物型方程解的振动准则[J].数学学报，2001，44(3):501–506.
[30] Qiu J. Exponential stability of impulsive neural networks with time-varying delaysand reaction-diffusion term[J]. Neurocomputing,2007,70:1102-1108.
[31] Li K. Song Q. Exponential stability of impulsive Cohen-Grossberg neural networkswith time-varying delays and reaction-diffusion term[J]. Neurocomputing,2008,1-3,(72):231-240.
[32] Li ZA, Li KL. Stability analysis of impulsive Cohen–Grossberg neural networkswith distributed delays and reaction–diffusion terms[J]. Applied MathematicalModeling,2009,33:1337–1348.
[33] Pan J, Liu XZ, Zhong SM. Stability criteria for impulsive reaction-diffusionCohen-Grossberg neural networks with time-varying delays[J]. Math. Comput.Modell.2010,51:1037-1050.
[34] Zhu W. Global exponential stability of impulsive reaction-diffusion equation withvariable delays[J]. Appl. Math. Comput.,2008,205:362-369.
[35] Pan J, Zhong SM. Dynamical behaviors of impulsive reaction-diffusionCohen-Grossberg neural network with delays[J]. Neurocomputing,2010,73:1344-1351.
[36]齐民友.线性偏微分算子引论(上册)[M].北京:科学出版社，1984.
[37]伍卓群，尹景学，王春朋.椭圆与抛物型方程引论[M].北京:科学出版社，2003.
[38]陈亚浙.二阶抛物型偏微分方程[M].北京:北京大学出版社，2003.
[39]王明新.非线性抛物型方程[M].北京:科学出版社，1997.
[40] Kallianpur G，Xiong J. Stochastic Differential Equationsin Infinite Dimensions[J].1995,26, IMS Lecture Notes, Hayward, California.
[41] Babugka I, Andersson B, Smith P J, Levin K. PartI: Statistical analysis on fiberscale[J]. Comput. Methods Appl. Mech. Engrg.1999,172:27-77.
[42] Elishakoff I, Ren Y. The bird's eye view on finite element method for structureswith large stochastic variations[J]. Comput. Methods Appl. Mech. Engrg.1999,168:51-61.
[43] Ghanem RG, Kruger R M. Numerical solution of spectral stochastic finite elementsystems[J]. Comput. Methods Appl. Mech. Engrg.,1996,129:289-303.
[44] Taniguchi T. Almost sure exponential stability for stochastic partial functionaldifferential equations[J]. Stochastic Anal. Appl.1998,16(5):965-975.
[45]罗琦，邓飞其，包俊东.一类随机分布参数系统反馈控制的镇定[J].控制理论与应用,2005,22(3):477-480.
[46]赵碧蓉邓飞其罗琦.中立型分布参数随机系统的指数稳定性[J].华南理工大学学报,2004,32(12):70-74.
[47] Park Ju H, yun H, Cho J. A delay-dependent asymptotic stability criterion ofcellular neural networks with time-varying discrete and distributed delays[J].Chaos, Solitons and Fractals,2007,33:436-442.
[48] Cao J, Wang J. Global asymptotic and robust stability of recurrent neural networkswith time delays[J]. IEEE Transactions on Circuits and Systems I: FundamentalTheory and Applications,2005,52(2):417–426.
[49]王占山.连续时间时滞递归神经网络的稳定性[M].沈阳:东北大学出版社,2007.
[50] Wu RC. Exponential convergence of BAM neural networks with time-varyingcoefficients and distributed delays[J]. Nonlinear Analysis: RWA,2010,11:562-73.
[51] Zou F, Nossek JA. Bifurcation and chaos in cellular neural networks[J]. IEEETrans Circuits and Systems I1993,40:166-173.
[52] Lu HT. Chaotic attractors in delayed neural networks [J]. Physics Letters A,2002,298:109-119.
[53] Song QK, Cao JD, Zhao ZJ. Periodic solutions and its exponential stability ofreaction–diffusion recurrent neural networks with continuously distributeddelays[J]. Nonlinear Anal., Real World Appl.2006,7:65–80.
[54] Liang JL, Cao JD. Global exponential stability of reaction–diffusion recurrentneural networks with time-varying delays[J]. Phys. Lett. A,2003,314:434–442.
[55] Song QK, Zhao ZJ, Li YM. Global exponential stability of BAM neural networkswith distributed delays and reaction–diffusion terms[J]. Phys Lett A,2005,335:213–225.
[56] Wang ZS., Zhang HG., Li P. An LMI Approach to Stability Analysis ofReaction–Diffusion Cohen–Grossberg Neural Networks Concerning DirichletBoundary Conditions and Distributed Delays[J]. IEEE Trans. Syst. Man Cybern. B,2010,40:1596-1606.
[57] Wang LS, Zhang RJ, Wang YF. Global exponential stability of reaction–diffusioncellular neural networks with S-type distributed time delays[J]. Nonlinear Analysis:RWA,2009(10):1001–1113.
[58] Zhang WY, Li JM. Global exponential stability of reaction–diffusion neuralnetworks with discrete and distributed time-varying delays[J]. Chin. Phys. B,2011,20(3):030701.
[59] Lu J. Robust global exponential stability for interval reaction-diffusion Hopfieldneural networks with distributed delays[J]. IEEE Trans Circ Syst II2007,54:1115–1119.
[60]楼旭阳,崔宝同.一类分布参数动态系统的周期性分析[J].自动化学报，2009，35(1):77-84.
[61]邓飞其，赵碧蓉，罗琦.具分布参数的随机Hopfield神经网络的指数稳定[J]，控制理论与应用,2005,22(2):196-200.
[62]罗琦，邓飞其，包俊东，赵碧蓉，傅予力.具分布参数的随机Hopfield神经网络的镇定[J].中国科学(E辑)，2004,34(6):619-628.
[63] Zhu Q, Li X., Yang XS. Exponential stability for stochastic reaction–diffusionBAM neural networks with time-varying and distributed delays[J]. Appl. Math.and Comput.2011,217:6078-6091.
[64]罗琦，邓飞其，包俊东.随机分布参数型Hopfield时滞神经网络的稳定[J].数学物理学报，2006,26A(6)：968-977.
[65]罗琦，邓飞其，毛学荣，包俊东，张雨田.随机反应扩散系统稳定性的理论与应用[J].中国科学(E辑)，2007,37(10):1272-1284.
[66] Xu X, Zhang J， Zhang W. Mean square exponential stability of stochastic neuralnetworks with reaction-diffusion terms and delay[J]. Appl. Math. Lett.2011,(24):5-11.
[67]廖晓昕.稳定性的数学理论和应用[M].武汉:华中师范大学出版社，2001.
[68]黄琳.稳定性理论[M].北京:北京大学出版社2001.
[69]钱学森，宋健.工程控制论[M].上下册科学出版社，1980，1981.
[70]廖晓昕.动力系统的稳定性理论和应用[M].北京:国防工业出版社，2000.
[71] Amraoui S, Rhali SL. Monotonicity and stability for some reaction-diffusionsystems with and Dirichlet boundary conditions [J]. J. Math. Anal. Appl.,2001,255:458-479.
[72] Ahmad S, Rao MR. Stability of Volttera diffusion equations with time delays [J].Appl. Math. Comput.,1998,90:143-154.
[73] Farkas G, Sinom PL., Stability properties of positive solutions to partial differentialequations with delay[J]. Electronic J. Diff. Equs.,2001(64):1-8.
[74] Simon H.神经网络原理[M].叶世伟，史忠植(译).北京:机械工业出版社，2004.
[75]钟守铭,刘碧森，王晓梅，范小明，神经网络稳定性理论[M].北京:科学出版社，2008.
[76] Rakkiyappan R., Balasubramaniam P. Delay-dependent asymptotic stability forstochastic delayed recurrent neural networks with time varying delays [J]. Appl.Math. Comput.2008,198:526–533.
[77] Huang CX., Cao JD. Convergence dynamics of stochastic Cohen-Grossberg neuralnetworks with unbounded distributed delays [J]. IEEE Trans. Neural Netw.,201122:561-572.
[78] Zhang C. Dynamic analysis of reaction–diffusion Cohen–Grossberg neuralnetworks with varying delays and Robin boundary conditions [J]. Chaos, Solitonsand Fractals2009,42:1724–1730.
[79] Zhang ZQ, Yang Y, Huang YS. Global exponential stability of interval generalBAM neural networks with reaction–diffusion terms and multiple time-varyingdelays [J]. Neural Networks,2011,24:457-465.
[80] Yang ZG, Xu DY. Global dynamics for non-autonomous reaction-diffusion neuralnetworks with time-varying delays [J]. Theoretical Computer Science,2008,403:3–10.
[81] Song QK, Cao JD. Global exponential robust stability of Cohen–Grossberg neuralnetworks with time-varying delays and reaction–diffusion terms [J]. Journal of theFranklin Institute2006,343:705-719.
[82] Liu PC, Qiang Y. etc. Analysis on global exponential robust stability ofreaction–diffusion neural networks with S-type distributed delays[J]. Physica D:Nonlinear Phenomena,2008,237:475–485.
[83] Wang LS, Zhang Y, Zhang Z, Wang YF. LMI-based approach for globalexponential robust stability for reaction–diffusion uncertain neural networks withtime-varying delay [J]. Chaos, Solitons and Fractals2009,41:900–905.
[84] Balasubramaniam P, Vidhya C. Global asymptotic stability of stochastic BAMneural networks with distributed delays and reaction-diffusion terms[J]. Journal ofComputational and Applied Mathematics,2010,234:3458-3466.
[85] Karimi H, Gao H. New delay-dependent exponential H∞synchronization foruncertain neural networks with mixed time delays[J]. IEEE Transactions onSystems Man, and Cybernetics-Part B: Cybernetics,2010,40:173–185.
[86] Pecora LM, Carroll TL. Synchronization in chaotic systems [J]. Physical ReviewLetters,1990,64:821-824
[87] K.Aihara, Takabe T., Toyoda M. Chaotic neural networks[J]. Physics Letters A,1990,144:333-340
[88] Balasubramaniam P, Chandran R, Jeeva Sathya Theesar S. Synchronization ofchaotic nonlinear continuous neural networks with time-varying delay[J].Cognitive Neurodynamics,2011,(5):361–371.
[89] He W, Cao JD. Adaptive synchronization of a class of chaotic neural networkswith known or unknown parameters[J]. Physics Letters A,2008,372:408–416.
[90] Milanovic V, Zaghloul M. Synchronization of chaotic neural networksandapplications to communications[J]. International Journal of Bifurcation and Chaos,1996,6:2571–2585.
[91] Hu C., Yu J., Jiang H., Teng, Z. Exponential lag synchronization for neuralnetworks with mixed delays via periodically intermittent control[J]. Chaos,2010,20:023108.
[92] Barsella A, Lepers C. Chaotic lag synchronization and pulse lasers coupled bysaturableabsorber [J]. Optics Communications,2002,205:397-403.
[93] Shahverdiev EM, Sivaprakasam S., Shore KA. Lag synchronization intime-delayed systems[J]. Physics Letters A,2002,292(6):320-324.
[94] Gilles Renversez. Synchronization in two neurons: Results for model withtime-delayedinhibition[J]. Physica D,1998,114:147-171.
[95] S. Arkady. Pikovsky, Michael G. Rosenblum, Grigory V. Osipov. Kurths, Jürgen.Phase synchronization of chaotic oscillators by external driving[J]. Physica D,1997,104:219-238.
[96] R. Mainieri, J. Rehacek. Projective synchronization in three-dimensional chaoticsystems[J]. Physical Review Letters,82(1999):3042-3045.
[97] Voss HU. Anticipating chaotic synchronization[J]. Physical Review E,2000,61(5):5115-5119.
[98] Boccaletti S, Kurths J, Osipov G, Valladares DL., Zhou CS. The synchronizationof chaotic systems[J]. Physics Reports,2002,366:1-101.
[99] Carrol TL, Pecora LM. Synchronization of chaotic circuits [J]. IEEE Trans Circuitsand Systems,1991,38:453-456.
[100] Pecora L M, Carroll T L. Cascading synchronized chaotic systems [J]. Physica D,1993,67:126-140.
[101] Wang Y, Cao JD. Synchronization of a class of delayed neural networks withreaction–diffusion terms[J]. Physics Letters A,2007,369:201–211.
[102] Zhang WY, Li JM. Global exponential synchronization of delayed BAM neuralnetworks with reaction-diffusion terms and the Neumann boundary conditions[J].Boundary Value Problems2012(2): doi:10.1186/1687-2770-2012-2.
[103] Gan QT. Global exponential synchronization of generalized stochastic neuralnetworks with mixed time delays and reaction-diffusion terms[J].Neurocomputing,2012,89:96-105.
[104] Wang K. Teng ZD. Jiang HJ. Global exponential synchronization in delayedreaction-diffusion cellular neural networks with the Dirichlet boundaryconditions[J].Math. Comput. Modell,2010,52:12-24.
[105] Lou XY, Cui BT. Asymptotic synchronization of a class of neural networks withreaction-diffusion terms and time-varying delays [J]. Computers Math. Appl.,2006,52:897-904.
[106] Wang Y, Cao JD. Synchronization of a class of delayed neural networks withreaction-diffusion terms[J]. Phys. Lett. A,2007,369:201-211.
[107] Hu C, Yu J, Jiang H, Teng Z. Exponential synchronization for reaction–diffusionnetworks with mixed delays in terms of p-norm via intermittent driving[J].Neural Networks,2012,31:1–11.
[108] Shi G, Ma Q. Synchronization of stochastic Markovian jump neural networkswith reaction-diffusion terms[J]. Neurocomputing,2012,77:275–280.
[109] Gan QT. Exponential synchronization of stochastic Cohen–Grossberg neuralnetworks with mixed time-varying delays and reaction–diffusion via periodicallyintermittent control[J]. Neural Networks,2012,31:12–21.
[110] S. Sivaprakasam, Shahverdiev EM, Spencer PS, Shore KA. ExperimentalDemonstration of Anticipating Synchronization in Chaotic Semiconductor Laserswith Optical Feedback[J]. Physical Review Letters,2001,86,15401-1-3.
[111] John JK, Amritkar RE. Synchronization of unstable orbits using adaptive control[J]. Physical Review E,1994,49:4843-4848.
[112] Sheng L, Yang H, Lou XY. Adaptive exponential synchronization of delayedneural networks with reaction-diffusion terms[J]. Chaos, Solitons and Fractals,2009,40:930-939.
[113] Yang T, Chua L. Impulsive control and synchronization of nonlinear dynamicalsystemsand application to secure communication [J]. International Journal ofBifurcation and Chaos,1997,7:645-664.
[114] Hu C, Jiang HJ, Teng ZD. Impulsive control and synchronization for delayedneural networks with reaction-diffusion terms[J]. IEEE Trans Neural Netw,2010,21:67-81.
[115] Nicaise S, Pignotti C. Stability and Instability Results of the Wave Equationwith a Delay Term in the Boundary or Internal Feedbacks[J]. SIAM Journal onControl and Optimization,2006,45(5):1561-1585.
[116] Cao JD, Wang J. Global exponential stability and periodicity of recurrent neuralnetworks with time delays[J]. IEEE Trans Circ Syst I,2005,52:920–931.
[117] Arik S, Orman Z. Global stability analysis of Cohen-Grossberg neural networkswith time-varying delays[J]. Phys. Lett. A,2005,341:410–421.
[118] Chen T, Rong L. Delay-independent stability analysis of Cohen–Grossberg neuralnetworks[J]. Phys. Lett. A,2003,317:436-449.
[119] He Y, Wu M, She J, Liu G. Delay-dependent robust stability criteria for uncertainneutral systems with mixed delays[J]. Systems and Control Letters,2004,51(1):57-65.
[120] Gu K., Kharitonov V., Chen J. Stability of Time-Delay Systems[J]. Birkhauser,Boston,2003.
[121] Liao XX, Yang SZ, Cheng SJ., Fu YL. Stability of generalized networks withreaction-diffusion terms [J]. Sci. China Ser. F,2001,44:87–94.
[122]廖晓昕,傅予力等.具有反应扩散项的Hopfield神经网络的稳定性[J].电子学报,2000,28:78～82.
[123] Lee SM，Kwon OM，Ju H. Park. A new approach to stability analysis of neuralnetworks with time-varying delay via novel Lyapunov--Krasovskii functional[J].Chin. Phys. B,2010,19(5):50507.
[124] Arena P, Fortuna L, Branciforte M. Reaction–diffusion CNN algorithmstogenerate and control artificial locomotion[J]. IEEE Transactions on Circuits andSystems I,1999,46:253–260.
[125] Ensari T, Arik S. Global stability analysis of neural networks with multiple timevarying delays[J]. IEEE Transactions on Automatic Control,2005,50(11):1781–1785.
[126] Erbe L H, et al. Comparison principles for impulsive parabolic equations withapplications to models of single species growth [J]. J Austral Math Soc, Ser B,1991,32(4):382-400.
[127] Haykin S, Neural Networks[M]. Prentice-Hall, NJ,1994.
[128] Vidhya C, Balasubramaniam P. On the stability of the stochastic parabolic Itoequation with delay and Markovian jump[J]. Computers and Mathmatics withApplications,2010,60:1959-1963.
[129] Boccaletti S, Kurths J., Osipov G., Valladares DL., Zhou CS. Thesynchronization of chaotic systems[J]. Physics Reports,2002,366:1-101.
[130] Li XD. Existence and global exponential stability of periodic solution forimpulsive Cohen–Grossberg-type BAM neural networks with continuouslydistributed delays[J]. Applied Mathematics and Computation2009,215:292–307.
[131] Hardy GH, Littlewood JE, Polya G. Inequalities, second edition[M]. CambridgeUniv. Press, London,1952.
[132] Mao XR. Stochastic Differential Equation and Application [M]. HorwoodPublishing, Chichester,1997.
[133] Li ZA, Li KL. Stability analysis of impulsive Cohen–Grossberg neural networkswith distributed delays and reaction–diffusion terms[J]. Applied MathematicalModeling,2009,33:1337–1348.
[134] Huang CX, Cao JD. On pth moment exponential stability of stochasticCohen–Grossberg neural networks with time-varying delays[J]. Neurocomputing,2010,73:986–990.
[135] Wang XH, Guo QY, Xu DY. Exponential p-stability of impulsive stochasticCohen–Grossberg neural networks with mixed delays[J]. Math. Comput. Simulat.2009,79:1698–1710.
[136] Rong LB, LMI approach for global periodicity of neural networks withtime-varying delays[J]. IEEE Trans. on Circuits and Systems I: Regular papers,2005,52(7):1451-1458.
[137]廖晓昕,昌莉,沈轶，离散Hopfield神经网络的稳定性研究.自动化学报,1999,25(6):721-727.
[138] Zhang Y, Pheng H A, Vadakkpepat P, Absolute periodicity and absolute stabilityof delayed neural networks[J]. IEEE Trans. on Circuits and System I:Fundamental Theory and Applications,2002,49(2):256-261.
[139] Cao J, Wang L. Exponential stability and Periodic oscillatory solution in BAMnetowrks with delays[J]. IEEE Trans. on Neura1Networks,2002,13(2):457-463.
[140]盛立,杨慧中,楼旭阳.具有漏泄时滞的的高阶细胞神经网络的的多周期性分析[J].控制理论与应用，2010,27(1):103-106.
[141] Civalleri P, Gilli M. Practical stability criteria for cellular neu-ral networks[J].Electronics Letters,1997,33(11):970–971.
[142] Cao JD, Feng G, Wang Y. Multistability and multiperiodicity of delayedCohen-Grossberg neural networks with a general class of activation functions[J].Physica D,2008,237(13):1734–1749.
[143] Pan J., Zhan YX. On periodic solutions to a class of non-autonomously delayedreaction-diffusion neural networks[J]. Commun Nonlinear Sci Numer Simulat2011,16:414-422.
[144] Lv Y, Lv W, Sun J. Convergence dynamics of stochastic reaction-diffusionrecurrent neural networks with continuously distributed delays[J]. NonlinearAnal. RWA.,2008(9):1590-1606.
[145] Lu J, Lu L. Global exponential stability and periodicity of reaction-diffusionrecurrent neural networks with distributed delays and Dirichlet boundaryconditions[J]. Chaos, Solitons and Fractals2009,39:1538–1549.
[146] Li X. Existence and global exponential stability of periodic solution for delayedneural networks with impulsive and stochastic effects[J]. Neurocomputing,2010,73:749-758.
[147] V. Lakshmikantham, S. Leela. Differential and Integral Inequalities[M]. NewYork: Academic,1969.
[148] Liang J, Wang Z, Liu Y, Liu X. Global synchronization control of generaldelayed discrete-time networks with stochastic coupling and disturbances[J].IEEE Trans. Syst. Man and Cybern. B Cybern,2008,38:1073-1083.
[149] Zhou QH, Wan L, Sun JH. Exponential stability of reaction–diffusion generalizedCohen–Grossberg neural networks with time-varying delays [J]. Chaos, Solitonsand Fractals2007,32:1713–1719.
[150] Luo XY, Cui BT. Boundedness and exponential stability for nonautonomouscellular neural networks with reaction–diffusion terms [J]. Chaos, Solitons andFractals2007,33:635–62.
[151] Cui BT, Luo XY. Global exponential stability of BAM neural networks withdistributed delays and reaction–diffusion terms [J]. Chaos, Solitons and Fractals,2006,27:1347–1354.
[152] Wang L, Zhang Z, Wang Y. Stochastic exponential stability of the delayedreaction–diffusion recurrent neural networks with Markovian jumpingparameters[J]. Physics Letters A,2008,372:3201–3209.
[153]肖晓波,奚宏生,季海波.不确定Markov跳跃线性系统的鲁棒跟踪与模型跟随[J].控制与决策,2006,21(12):1432–1436.
[154] Xu SY, Chen TW． H∞output feedback control for uncertain stochastic systemswith time-varying delays[J]. Automatica,2004,40(12):2091-2098．
[155] Wang ZD，Lam J，Liu XH． Exponential filtering for uncertain Markovian jumptime-delay systems with nonlinear disturb-ances[J]. IEEE Trans on Circuits andSystems Part Ⅱ，2004,51(5):262-268．
[156] Shi P，Karan M，Kaya C Y．Robust Kalman filtering design for Markovian jumplinear systems with norm-bounded un-know n nonlinearties[J]．Circuits，Systemsand Signal Processing，2005，24(2):135-150．
[157] Boukas EK，Liu ZK． Robust stability and stability of Markov jump linearuncertain systems with mode-dependent time delays[J]. Journal of OptimizationTheory and Applications，2001，109(3):587-600．
[158] Liu YR, Wang ZD, Liu XH, Exponential synchronization of complex networkswith Markovian jump and mixed delays [J]. Phys. Lett. A,2008,372(22):3986-3998.
[159] Cao Y, Lam J. Robust H∞control of uncertain Markovian jump systems withtime-delay[J]. IEEE Transactions on Automatic Control,2000,45(1):77–83.
[160] Mao X. Exponential stability of stochastic delay interval systems with Markovianswitching[J]. IEEE Transactions on Automatic Control,2002,47(10):1604–1612.
[161] Xu S, Lam J. Delay-dependent H∞control and filtering for uncertain Markovianjump systems with time-varying delays[J]. IEEE Transactions on Circuits andSystem,2007,54(9):2070–2077.
[162] Xu S, Chen T, Lam J. Robust H∞filtering for uncertain Markovian jump systemswith mode-dependent time delays[J]. IEEE Trans-actions on Automatic Control,2003,48(5):900–907.
[163] Chen WH, Cu JX, Guan ZH. Guaranteed cost control for uncer-tain Markovianjump systems with mode-dependent time-delays[J], IEEE Transactions onAutomatic Control,2003,48(12):2270–2275.
[164] Shao HY. Delay-rang-dependent robust H∞filtering for uncertainstochasticsystems with mode-dependent time delays and Markovianjump parameters[J].Journal of Mathematical Analysis and Applications,2008,342(2):1084–1095.
[165] Zhu Q, Cao JD. Stability of Markovian jump neural networks with impulsecontrol and time varying delays[J]. Nonlinear Analysis: Real World Applications2012,13:2259–2270.
[166] Wang Y, Lin P, Wang L. Exponential stability of reaction–diffusion high-orderMarkovian jump Hopfield neural networks with time-varying delays[J].Nonlinear Analysis: Real World Applications2012,13:1353–1361.
[167] Zhang LX, Boukas EK. Stability and stabilization of Markovian jump linearsystems with partly unknown transition probabilities[J]. Automatica,2009,45(2),436-468.
[168] Zhang LX,. Boukas EK, Lam J. Analysis and synthesis of Markov jump linearsystems with time-varying delays and partially known transition probabilities[J].IEEE Transactions on Automatic Control,2009,53(10):2458-2464.
[169] Zhang Y, He Y, Wu M, Zhang J. Stabilization for Markovian jump systems withpartial information on transition probability based on free-connection weightingmatrices[J], Automatica,2011,47:79-84.
[170] X. Lou, Cui B. Stochastic stability analysis for delayed neural networks of neutraltype with Markovian jump parameters[J]. Chaos, Solitons and Fractals,2009,39(5):2188-2197.
[171] Teng L, Yan P. Dynamical behaviors of reaction–diffusion fuzzy neuralnetworks with mixed delays and general boundary conditions[J]. CommunNonlinear Sci Numer Simulat,2011,16:993-1001.
[172] Li T, Luo Q, Sun CY, Zhang BY. Exponential stability of recurrent neuralnetworks with time-varying discrete and distributed delays[J]. Nonlinear Anal.:RWA,2009(10):2581–2589.
[173] Sontag ED. Smooth stabilization implies coprime factorization[J], IEEETransaetions Automatic Control,1989,34:435–443.
[174] Kokotovie P., Areak M.. Constructive nonlinear control: a historical perspective[J]. Automatica,2001,37:637–662.
[175] Sontag ED, Wang Y. On charaeterizations of the input to state stability property[J].Systems and Control Letters,1995,24:351–559.
[176] Sontag ED，Wang Y. New echaraeterizations of the input to state stabilityproperty[J], IEEE Transactionson Automatic Control，1996,41:1283–1294..[177] Sontag ED. Comments on integral variants of ISS [J]. Systems and ControlLetters1998,34:93–100.
[178] Huang L, Mao X. On input-to-state stability of stochasticretarded systems withMarkovian switching[J]. IEEE Trans Automat Control,2009,54(8):1898–1902.
[179] Fridman E, Dambrine M, Yeganefar N， On input-to-state stability of systemswith time-delay: A matrix inequalities approach[J]. Automatica,2008,44:2364–2369.
[180] Yu W, Li X, Some stability properties of dynamic neural networks[J]. IEEETrans Circuits Syst I Fundam Theory Appl,2001,48(2):256–259.
[181] Sanchez EN, Perez JP，Input-to-state stability analysis for dynamic neuralnetworks[J]. IEEE Trans Circuits Syst I FundamTheory Appl,1999,46(11):1395–1398.
[182] Guo Y. New results on input-to-state convergence for recurrent neural networkswith variable inputs[J]. Nonlinear Anal RWA.2008(9):1558–1566.
[183] Ahn CK. Passive learning and input-to-state stability of switched Hopfield neuralnetworks with time-delay[J]. Inform Sci,2010,180:4582–4594.
[184] Zhu S, Shen Y. Two algebraic criteria for input-to-state stability of recurrentneural networks with time-varying delays[J]. Neural Comput and Applic,2012,23, DOI10.1007/s00521-012-0882-9.
[185] Adimurthi. Hardy-sobolev inequality in H1and its applications[J].Commun Contemp Math,2002(4):409-434.
[186] Wang T. Stability in Abstract Functional-differential equations[J]. II Applications.Journal of Mathematical Analysis and Applications.1994,186:835-861.
[187] Fridman E, Orlov Y. Exponential Stability of Linear Distributed ParameterSystems with Time-varying Delays[J]. Automatica,2009,45:194–201.
[188] Curtain R, Zwart H. An Introduction to Infinite-dimensional Linear Systems[M].1995, Springer-Verlag.
[189] Pazy A. Semigroups of Linear Operators and Application to Partial DifferentialEquations [M], New York:Springer-Verlag,1983.
[190] R. Temam. Infinite Dimensional Dynamical Systems in Mechanics and Physics.Springer-Verlag, New York, Berlin1998.
[191] Sarasola C. Feedback synchronization of chaotic systems [J]. InternationalJournal of Bifurcation and Chaos,2003,13:177-191.
[192] Salarieh H，Shahrokhi M．Adaptive synchronization of two different chaoticsystems with time varying unknown parameters[J]．Chaos，Solitons andFractals，2008，37(1)：125-136．
[193] Sun FY, Zhao Y, Zhou TS．Identify fully uncertain parameters and designcontrollers based on synchronization[J]. Chaos, Solitons and Fractals，2007，34(5)：1677-1682．
[194] Park JH．Adaptive modified projective synchronization of a unified chaoticsystem with all uncertain parameter[J]. Chaos，Solitons and Fractals，2007，34(5)：1552-1559．
[195] LI Z，Jiao L，Lee JJ. Robust adaptive global synchronization of complexdynamical networks by adjusting time-varying coupling strength. Physica A,2008,387:1369-1380.
[196] Chen L，Wu L，Zhua S. Synchronization in complex networks by adjustingtime-varying couplings. Eur.Phys. J. D,2008,48:405-409.
[197] Huang LH， Wang ZY, Wang YN. Synchronization analysis of delayed complexnetworks via adaptive time-varying coupling strengths. Physics Letters A，2009，373:3952–3959.
[198] Guo XY, Li JM, A new synchronization algorithm for delayed complex dynamicalnetworks via adaptive control approach, Commun Nonlinear Sci Numer Simulat,2012,17(11):4395-4403.
[199] Hale JK, Theory of functional differential equation[M]. New York:Springer-Verlag,1977.
[200] Allegretto W., Papini D. Stability for delayed reaction–diffusion neural networks[J]. Physics Letters A,2007,360,669–680.
[201]叶其孝、李正元著，反应扩散方程引论[M]，科学出版社，1999年，北京.
[202] Zhang X., Wu S., Li KL. Delay-dependent exponential stability for impulsiveCohen–Grossberg neural networks with time-varying delays and reaction–diffusionterms[J]. Commun Nonlinear Sci Numer Simulat,2011,16:1524–1532.
[203] Bainov D, Kdzislaw ZZ, Minchev E. Monotone iterative methods for impulsivehyperbolic differential functional equations[J]. J. Comput. Appl. Math.,1996,70:329-347.
[204]燕居让.脉冲中立型时滞微分方程的振动性[J].数学年刊,2000,21A (6):755-762.
[205] Zhang WY, Li JM, Shi NZ. Stability analysis for stochastic Markovian jumpreaction–diffusionneural networks with partially known transition probabilitiesand mixed time delays[J]. Discrete Dynamics in Nature and Society,2012,2012:1-17.