分数阶Cohen-Grossberg神经网络的Mittag-Leffler稳定性
|
摘要
在整数阶Cohen-Grossberg神经网络与分数阶理论及分数阶神经网络的基础上,提出了分数阶Cohen-Grossberg神经网络。为了研究该类型神经网络,引入Mittag-Leffler函数并利用Mittag-Leffler函数及分数阶导数的相关性质,进而通过构造Lyapunov函数的方法,研究了分数阶Cohen-Grossberg神经网络的Mittag-Leffler稳定性,并最终给出了相应的充分性条件。最后,通过实例仿真验证了结论的正确性。
On the basis of the integer order Cohen-Grossberg neural networks and fractional order Hopfield neural networks, the fractional order Cohen-Grossberg neural networks were given. In order to research this type neural networks,Mittag-Leffler function was brought, and making use of the property of the Mittag-Leffler function and fractional order derivative, the Mittag-Leffler stability of fractional order Cohen-Grossberg neural networks was investigated by constructing Lyapunov function, and a sufficient condition was gotten. At last, the correctness of the conclusion was verified by an emulating example.
On the basis of the integer order Cohen-Grossberg neural networks and fractional order Hopfield neural networks, the fractional order Cohen-Grossberg neural networks were given. In order to research this type neural networks,Mittag-Leffler function was brought, and making use of the property of the Mittag-Leffler function and fractional order derivative, the Mittag-Leffler stability of fractional order Cohen-Grossberg neural networks was investigated by constructing Lyapunov function, and a sufficient condition was gotten. At last, the correctness of the conclusion was verified by an emulating example.
引文
[1]COHEN M,GROSSBERG S.Absolute stability of global pattern formation and parallel memory storage by competitive neural networks[J].IEEE Transactions on Systems,Man and Cybernetics,1983,13(5):815-826.
[2]ZHANG H G,JI C.Delay-independent globally asymptotic stability of Cohen-Grossberg neural networks[J].International Journal of Information and Systems Sciences,2005,1(3-4):221-228.
[3]JI C,ZHANG H G,Wei Y.LMI approach for global robust stability of Cohen-Grossberg neural networks with multiple delays[J].Neurocomputing,2008,71(4-6):475-485.
[4]AREFEH B,MOHAMMAD B M.Fractional-order hopfield neural networks[C]//International Conference on Advances in Neuro-information Processing.Berlin:Springer,2009:883-890.
[5]ZOU T,QU J F,CHEN L P,et al.Stability analysis of a class of fractional-order neural networks[J].Indonesian Journal of Electrical Engineering,2014,12(2):1086-1093.
[6]ABDULAZIZ ALOFI,CAO J D,AHMED ELAIW,et al.Delay-dependent stability criterion of caputo fractional neural networks with distributed delay[J].Discrete Dynamics in Nature and Society,2014,2014:1-6.
[7]孙校书,刘孝磊,盖明久.一类分数阶BAM神经网络的Mittag-Leffler稳定性[J].重庆师范大学学报:自然科学版,2016,33(6):54-57.SUN XIAOSHU,LIU XIAOLEI,GAI MINGJIU.MittagLeffler stability analysis of a class of fraction-order BAMneural networks[J].Journal of Chongqing Normal University:Natural Science,2016,33(6):54-57.(in Chinese)
[8]刘孝磊,周刚,赵文飞.分数阶BAM神经网络的鲁棒稳定性[J].黑龙江大学自然科学学报,2015,32(6):728-734.LIU XIAOLEI,ZHOU GANG,ZHAO WENFEI.The robust stability of fraction-order BAM neural networks[J].Journal of Natural Science of Heilongjiang University,2015,32(6):728-734.(in Chinese)
[9]PODLUBNY I.Fractional differential equations[M].San Diego:Academic Press,1999:198-224.
[10]KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and applications of fractional differential equations[M].Amsterdam:Elsevier,2006:154-166.
[11]LI Y,CHEN Y,PODLUBNY I.Stability of fractional-order nonlinear dynamic systems:lyapunov direct method and generalized mittag-leffler stability[J].Computers&Mathematics with Applications.2010,59(5):1810-1821.
[12]ZHANG S,YU Y G,HU W.Robust stability analysis of fractional-order hopfield neural networks with parameter uncertainties[J].Mathematical Problems in Engineering,2014:1-14.
[13]CHEN J J,ZENG Z G,JIANG P.Global mittag-leffler stability and synchronization of memristor-based fractional-order neural networks[J].Neural Networks,2014(51):1-8.
[14]W CHEN,G PANG.A new definition of fractional Laplacian with application to modeling three-dimensional nonlocal heat conduction[J].Journal of Computational Physics,2016(309):350-367.
[15]DENG W H,LI C P,LU J H.Stability analysis of linear fractional differential system with multiple time-delays[J].Nonlinear Dynamic,2007(48):409-416.
[16]LIANG YINGJIE,CHEN WEN,RICHARD L.Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation[J].Physica A:Statistical Mechanics&Its Applications,2016(453):327-335.
[2]ZHANG H G,JI C.Delay-independent globally asymptotic stability of Cohen-Grossberg neural networks[J].International Journal of Information and Systems Sciences,2005,1(3-4):221-228.
[3]JI C,ZHANG H G,Wei Y.LMI approach for global robust stability of Cohen-Grossberg neural networks with multiple delays[J].Neurocomputing,2008,71(4-6):475-485.
[4]AREFEH B,MOHAMMAD B M.Fractional-order hopfield neural networks[C]//International Conference on Advances in Neuro-information Processing.Berlin:Springer,2009:883-890.
[5]ZOU T,QU J F,CHEN L P,et al.Stability analysis of a class of fractional-order neural networks[J].Indonesian Journal of Electrical Engineering,2014,12(2):1086-1093.
[6]ABDULAZIZ ALOFI,CAO J D,AHMED ELAIW,et al.Delay-dependent stability criterion of caputo fractional neural networks with distributed delay[J].Discrete Dynamics in Nature and Society,2014,2014:1-6.
[7]孙校书,刘孝磊,盖明久.一类分数阶BAM神经网络的Mittag-Leffler稳定性[J].重庆师范大学学报:自然科学版,2016,33(6):54-57.SUN XIAOSHU,LIU XIAOLEI,GAI MINGJIU.MittagLeffler stability analysis of a class of fraction-order BAMneural networks[J].Journal of Chongqing Normal University:Natural Science,2016,33(6):54-57.(in Chinese)
[8]刘孝磊,周刚,赵文飞.分数阶BAM神经网络的鲁棒稳定性[J].黑龙江大学自然科学学报,2015,32(6):728-734.LIU XIAOLEI,ZHOU GANG,ZHAO WENFEI.The robust stability of fraction-order BAM neural networks[J].Journal of Natural Science of Heilongjiang University,2015,32(6):728-734.(in Chinese)
[9]PODLUBNY I.Fractional differential equations[M].San Diego:Academic Press,1999:198-224.
[10]KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and applications of fractional differential equations[M].Amsterdam:Elsevier,2006:154-166.
[11]LI Y,CHEN Y,PODLUBNY I.Stability of fractional-order nonlinear dynamic systems:lyapunov direct method and generalized mittag-leffler stability[J].Computers&Mathematics with Applications.2010,59(5):1810-1821.
[12]ZHANG S,YU Y G,HU W.Robust stability analysis of fractional-order hopfield neural networks with parameter uncertainties[J].Mathematical Problems in Engineering,2014:1-14.
[13]CHEN J J,ZENG Z G,JIANG P.Global mittag-leffler stability and synchronization of memristor-based fractional-order neural networks[J].Neural Networks,2014(51):1-8.
[14]W CHEN,G PANG.A new definition of fractional Laplacian with application to modeling three-dimensional nonlocal heat conduction[J].Journal of Computational Physics,2016(309):350-367.
[15]DENG W H,LI C P,LU J H.Stability analysis of linear fractional differential system with multiple time-delays[J].Nonlinear Dynamic,2007(48):409-416.
[16]LIANG YINGJIE,CHEN WEN,RICHARD L.Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation[J].Physica A:Statistical Mechanics&Its Applications,2016(453):327-335.