一类时滞脉冲神经网络的稳定性分析
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摘要
时滞脉冲神经网络是时滞大系统的一个重要组成部分,具有十分丰富的动力学属性.鉴于它在信号处理、动态图像处理以及全局优化等问题中的重要应用,近年来,时滞脉冲神经网络的动力学问题引起了学术界的广泛关注.尤其是时滞脉冲神经网络平衡点的全局稳定性(包括全局渐近稳定性、全局指数稳定性等)得到了深入的研究,也获得了一系列深刻的结果.本文主要对一类时滞脉冲神经网络(即Hopfield神经网络)平衡点的全局渐近稳定性或全局指数稳定性进行了一系列的研究,取得了一些较深刻的结果.具体地说,本论文涉及到如下内容：
(1)非Lipschitz神经元激励下时滞脉冲神经网络
几乎所有现存的文献是基于Lipschitz神经元激励下研究时滞脉冲神经网络的稳定性问题.然而,很少研究非Lipschitz神经元激励下时滞脉冲神经网络的稳定性.基于此,本文主要对一类非Lipschitz神经元激励下时滞脉冲神经网络全局稳定性进行了一系列的研究,获得的一些新的结果.
(2)时滞脉冲神经网络的稳定性分析
运用同胚映射理论、拓扑度理论和Lyapunov泛函方法,得到了一些新的具有较少约束的全局渐近稳定性或全局指数稳定性判据,改进了现有的结果.
(3)脉冲对时滞神经网络稳定性的影响
针对当前许多时滞脉冲神经网络的稳定性判据均要求原时滞系统Lyapunov稳定的弊端,我们运用不等式技巧,得到了一些保证系统全局稳定的充分条件,放宽了对脉冲强度的限制,这对实际时滞脉冲系统的设计具有较强的指导作用.
As an important part of the delayed large systems, the delayed neural networks with impulses may exhibit the rich and colorful dynamical behaviors. Due to their important applications in signal processing, image processing as well as optimizing problems, the dy-namical issues of delayed neural networks with impulses have attracted worldwide attention in recent years. Recently, many interesting stability criteria for the equilibriums of delayed neural networks with impulses have been derived via Lyapunov function/functional method. A series of significative results have been obtained. This thesis mainly focuses on the global stability for a type of delayed neural networks with impulse. Specifically, the main contents are as follows:
(1) Non-Lipschitz Neuron Activations for Delayed Neural Networks with Impulses
Most existing results on stability for neural networks with impulses were obtained under some special assumptions on neuron activation functions, such as Lipschitz conditions. Cor-respondingly, there is not much work dedicated to investigate the stability of neural networks with non-Lipschitz neuron activations. The objective of this thesis is to study the stability of a class of delayed impulsive neural networks with non-Lipschitz neuron activations. Our results obtained in this thesis provide new sufficient criteria for a class of delayed impulsive neural networks developed by us.
(2) Stability Analysis for Delayed Neural Networks with Impulses
Several novel global asymptotical stability/global exponential stability criteria with less restriction are established by employing homeomorphism theory, topological degree theory and Lyapunov functional method, our obtained criteria improves the existing result.
(3) Effects of Impulses on Stability of Delayed Neural Networks
We investigate the global stability conditions of the delayed neural networks with im-pulses by means of inequality techniques. And the results overcome the restriction that the original neural network should be Lyapunov stable. The impulsive strength or impulse inter-val can be estimated by applying the proposed results.
(1)非Lipschitz神经元激励下时滞脉冲神经网络
几乎所有现存的文献是基于Lipschitz神经元激励下研究时滞脉冲神经网络的稳定性问题.然而,很少研究非Lipschitz神经元激励下时滞脉冲神经网络的稳定性.基于此,本文主要对一类非Lipschitz神经元激励下时滞脉冲神经网络全局稳定性进行了一系列的研究,获得的一些新的结果.
(2)时滞脉冲神经网络的稳定性分析
运用同胚映射理论、拓扑度理论和Lyapunov泛函方法,得到了一些新的具有较少约束的全局渐近稳定性或全局指数稳定性判据,改进了现有的结果.
(3)脉冲对时滞神经网络稳定性的影响
针对当前许多时滞脉冲神经网络的稳定性判据均要求原时滞系统Lyapunov稳定的弊端,我们运用不等式技巧,得到了一些保证系统全局稳定的充分条件,放宽了对脉冲强度的限制,这对实际时滞脉冲系统的设计具有较强的指导作用.
As an important part of the delayed large systems, the delayed neural networks with impulses may exhibit the rich and colorful dynamical behaviors. Due to their important applications in signal processing, image processing as well as optimizing problems, the dy-namical issues of delayed neural networks with impulses have attracted worldwide attention in recent years. Recently, many interesting stability criteria for the equilibriums of delayed neural networks with impulses have been derived via Lyapunov function/functional method. A series of significative results have been obtained. This thesis mainly focuses on the global stability for a type of delayed neural networks with impulse. Specifically, the main contents are as follows:
(1) Non-Lipschitz Neuron Activations for Delayed Neural Networks with Impulses
Most existing results on stability for neural networks with impulses were obtained under some special assumptions on neuron activation functions, such as Lipschitz conditions. Cor-respondingly, there is not much work dedicated to investigate the stability of neural networks with non-Lipschitz neuron activations. The objective of this thesis is to study the stability of a class of delayed impulsive neural networks with non-Lipschitz neuron activations. Our results obtained in this thesis provide new sufficient criteria for a class of delayed impulsive neural networks developed by us.
(2) Stability Analysis for Delayed Neural Networks with Impulses
Several novel global asymptotical stability/global exponential stability criteria with less restriction are established by employing homeomorphism theory, topological degree theory and Lyapunov functional method, our obtained criteria improves the existing result.
(3) Effects of Impulses on Stability of Delayed Neural Networks
We investigate the global stability conditions of the delayed neural networks with im-pulses by means of inequality techniques. And the results overcome the restriction that the original neural network should be Lyapunov stable. The impulsive strength or impulse inter-val can be estimated by applying the proposed results.
引文
1. Liu B, Huang L. Existence and stability of almost periodic solutions for shunting in-hibitory cellular neural networks with continuously distributed delays [J]. Physics Let-ters A,2006,349:177-186.
2. Xia Y, Cao J, Huang Z. Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses [J]. Chaos, Soli tons and Fractals,2007,34:1599-1607.
3. Zhou Q, Xiao B, Yu Y, Peng L. Existence and exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays[J]. Chaos, Solitons and Fractals,2007,34:860-866.
4. Liu B. Almost periodic solutions for shunting inhibitory cellular neural networks with-out global Lipschitz activation functions [J]. Journal of Computational and Applied Mathematics,2007,203:159-168.
5. Liu B, Huang L. Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays[J]. Chaos, Solitons and Fractals,2007,31:211-217.
6. Liu Y, You Z, Cao L. Almost periodic solution of shunting inhibitory cellular neural networks with time-varying and continuously distributed delays[J]. Physics Letters A, 2007,364:17-28.
7. Zhao W, Zhang H. On almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients and time-varying delays[J]. Nonlinear Analysis: Real World Applications,2008,9:2326-2336.
8. Ding H, Liang J, Xiao T. Existence of almost periodic solutions for SICNNs with time-varying delays[J]. Physics Letters A,2008,372:5411-5416.
9. Cai M, Zhang H, Yuan Z. Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays[J]. Mathematics and Computers in Simulation,2008,78:548-558.
10. Chen L, Zhao H. Global stability of almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients [J]. Chaos, Solitons and Fractals, 2008,35:351-357.
11. Shao J, Wang L, Ou C. Almost periodic solutions for shunting inhibitory cellular neural networks without global Lipschitz activaty functions[J]. Applied Mathemati-cal Modelling,2009,33:2575-2581.
12. Fink A. Almost periodic differential equations[M]. Berlin:Springer,1974.
13. Zhou L, Hu G. Global exponential periodicity and stability of cellular neural networks with variable and distributed delays [J]. Applied Mathematics and Computation,2008, 195:402-411.
14. Li T, Fei S. Stability analysis of Cohen-Grossberg neural networks with time-varying and distributed delays[J]. Neurocomputing,2008,71:1069-1081.
15. Zhang Q, Wei X, Xu J. Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays[J]. Chaos, Solitons and Fractals,2008,36:985-990.
16. Zhao W. Dynamics of Cohen-Grossberg neural network with variable coefficients and time-varying delays[J]. Nonlinear Analysis:Real World Applications,2008,9:1024-1037.
17. Xiong W, Zhou Q, Xiao B, Yu Y. Global exponential stability of cellular neural net-works with mixed delays and impulses[J]. Chaos, Solitons and Fractals,2007,34: 896-902.
18. Huang Z, Yang Q, Luo X. Exponential stability of impulsive neural networks with time-varying delays[J]. Chaos, Solitons and Fractals,2008,35:770-780.
19. Long S, Xu D. Delay-dependent stability analysis for impulsive neural networks with time-varying delays[J]. Neurocomputing,2008,71:1705-1713.
20. Wu H, Xue X. Stability analysis for neural networks with inverse Lipschitzian neuron activations and impulses[J]. Applied Mathematical Modelling,2008,32:2347-2359.
21. Song Q, Zhang J. Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays[J]. Nonlinear Analysis:Real World Applications, 2008,9:500-510.
22. Ahmada S, Stamov I. Global exponential stability for impulsive cellular neural net- works with time-varying delays[J]. Nonlinear Analysis,2008,69:786-795.
23. Tan M, Zhang Y. New sufficient conditions for global asymptotic stability of Cohen-Grossberg neural networks with time-varying delays[J]. Nonlinear Analysis:Real World Applications,2009,10:2139-2145.
24. Liu K, Zhang H. An improved global exponential stability criterion for delayed neural networks[J]. Nonlinear Analysis:Real World Applications,2009,10:2613-2619.
25. Wang Y. Global exponential stability analysis of bidirectional associative memory neural networks with time-varying delays[J]. Nonlinear Analysis:Real World Ap-plications,2009,10:1527-1539.
26. Idels L, Kipnis M. Stability criteria for a nonlinear nonautonomous system with de-lays[J]. Applied Mathematical Modelling,2009,33:2293-2297.
27. Wang J, Huang L, Guo Z. Dynamical behavior of delayed Hopfield neural networks with discontinuous activations [J]. Applied Mathematical Modelling,2009,33:1793-1802.
28. Li T, Guo L, Lin C, Sun C. New results on global asymptotic stability analysis for neural networks with time-varying delays [J]. Nonlinear Analysis:Real World Appli-cations,2009,10:554-562.
29. Kwon O, Park J. Improved delay-dependent stability criterion for neural networks with time-varying delays[J]. Physics Letters A,2009,373:529-535.
30. Souza F, Palhares R, Ekel P. Improved asymptotic stability analysis for uncertain de-layed state neural networks[J]. Chaos, Solitons and Fractals,2009,39:240-247.
31. Sun J, Liu G, Chen J, Rees D. Improved stability criteria for neural networks with time-varying delay[J]. Physics Letters A,2009,373:342-348.
32. Qiu F, Cui B, Wu W. Global exponential stability of high order recurrent neural net-work with time-varying delays[J]. Applied Mathematical Modelling,2009,33:198-210.
33. Liu B. Stability of shunting inhibitory cellular neural networks with unbounded time-varying delays[J]. Applied Mathematics Letters,2009,22:1-5.
34. Zhao H, Mao Z. Boundedness and stability of nonautonomous cellular neural networks with reaction-diffusion terms [J]. Mathematics and Computers in Simulation,2009,79: 1603-1617.
35. Yang D, Liao X, Hu C, Wang Y. New delay-dependent exponential stability criteria of BAM. neural networks with time delays [J]. Mathematics and Computers in Simulation, 2009,79:1679-1697.
36. Liu Z, Zhang H, Wang Z. Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays[J]. Neurocomputing,2009,72:1056-1064.
37. Chen Y, Wu Y. Novel delay-dependent stability criteria of neural networks with time-varying delay[J]. Neurocomputing,2009,72:1065-1070.
38. Li C, Feng G. Delay-interval-dependent stability of recurrent neural networks with time-varying delay [J]. Neurocomputing,2009,72:1179-1183.
39. Zhang B, Xu S, Zou Y. Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks withtime-varying delays [J]. Neurocomputing, 2008,72:321-330.
40. Yang D, Liao X, Chen Y, Guo S, Wang H. New delay-dependent global asymptotic stability criteria of delayed Hopfield neural networks [J]. Nonlinear Analysis:Real World Applications,2008,9:1894-1904.
41. Liao X, Yang J, Guo S. Exponential stability of Cohen-Grossberg neural networks with delays[J]. Communications in Nonlinear Science and Numerical Simulation,2008,13: 1767-1775.
42. Zhou Q, Wan L. Impulsive effects on stability of Cohen-Grossberg-type bidirectional associative memory neural networks with delays[J]. Nonlinear Analysis:Real World Applications,2009,10:2531-2540.
43. Li Z, Li K. Stability analysis of impulsive Cohen-Grossberg neural networks with distributed delays and reaction-diffusion terms [J]. Applied Mathematical Modelling, 2009,33:1337-1348.
44. Zhou J, Li S. Global exponential stability of impulsive BAM neural networks with distributed delays[J]. Neurocomputing,2009,72:1688-1693.
45. Zhou Q. Global exponential stability of BAM neural networks with distributed delays and impulses[J]. Nonlinear Analysis:Real World Applications,2009,10:144-153.
46. Xia Y, Wong P. Global exponential stability of a class of retarded impulsive differential equations with applications[J]. Chaos, Solitons and Fractals,2009,39:440-453.
47. Li D, Yang D, Wang H, Zhang X, Wan S. Asymptotical stability of multi-delayed cellular neural networks with impulsive effects[J]. Physica A,2009,388:218-224.
48. Li K, Song Q. Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms[J]. Neurocomputing,2008,72: 231-240.
49. Xia Y, Huang Z, Han M. Exponential p-stability of delayed Cohen-Grossberg-type BAM neural networks with impulses[J]. Chaos, Solitons and Fractals,2008,38:806-818.
50. Chen J, Cui B. Impulsive effects on global asymptotic stability of delay BAM neural networks[J]. Chaos, Solitons and Fractals,2008,38:1115-1125.
51. Zhou J, Li S, Yang Z. Global exponential stability of Hopfield neural networks with distributed delays[J]. Applied Mathematical Modelling,2009,33:1513-1520.
52. Chen S, Zhao W, Xu Y. New criteria for globally exponential stability of delayed Cohen-Grossberg neural network[J]. Mathematics and Computers in Simulation, 2009,79:1527-1543.
53. Wang Z, Liu Y, Liu X. State estimation for jumping recurrent neural networks with discrete and distributed delays[J]. Neural Networks,2009,22:41-48.
54. Cui B, Wu W. Global exponential stability of Cohen-Grossberg neural networks with distributed delays[J]. Neurocomputing,2008,72:386-391.
55. Li T, Luo Q, Sun C, Zhang B. Exponential stability of recurrent neural networks with time-varying discrete and distributed delays[J]. Nonlinear Analysis:Real World Ap-plications,2009,10:2581-2589.
56. Li T, Fei S, Guo Y, Zhu Q. Stability analysis on Cohen-Grossberg neural networks with both time-varying and continuously distributed delays[J]. Nonlinear Analysis: Real World Applications,2009,10:2600-2612.
57. Fang S, Jiang M, Wang X. Exponential convergence estimates for neural networks with discrete and distributed delays[J]. Nonlinear Analysis:Real World Applications, 2009,10:702-714.
58. Zhou Y, Zhong S, Ye M, Shi Z. Global asymptotic stability analysis of nonlinear dif-ferential equations in hybrid bidirectional associative memory neural network swith distributed time-varying delays[J]. Neurocomputing,2009,72:1803-1807.
59. Yu J, Zhang K, Fei S, Li T. Simplified exponential stability analysis for recurrent neural networks with discrete and distributed time-varying delays[J]. Applied Mathematics and Computation,2008,205:465-474.
60. Wu H, Shan C. Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses [J]. Applied Mathematical Modelling, 2009,33:2564-2574.
61. Wu A, Fu C. Exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying and distributed delays [J]. European Journal of Pure and Applied Mathematics,2009,2(3):448-461.
62. Fu C, Wu A. Global exponential stability of reaction-diffusion delayed BAM neural networks with Dirichlet boundary conditions[J]. Lecture Notes in Computer Science, 2009,5551:303-312.
63. Fu C, Wu A. Global exponential stability of delayed neural networks with non-Lipschitz neuron activations and impulses [J]. Lecture Notes in Computer Science, 2009,5821:92-100.
64. Fu C, Wu A. Almost periodic solutions for shunting inhibitory cellular neural net-works with time-varying and distributed delays[J]. Communications in Computer and Information Science,2009,51:162-170.
65. Fu C, Wu A. Global exponential stability of delayed FCNNs with reaction-diffusion terms[J]. Lecture Notes in Decision Sciences,2009,12(B):857-861.
2. Xia Y, Cao J, Huang Z. Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses [J]. Chaos, Soli tons and Fractals,2007,34:1599-1607.
3. Zhou Q, Xiao B, Yu Y, Peng L. Existence and exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays[J]. Chaos, Solitons and Fractals,2007,34:860-866.
4. Liu B. Almost periodic solutions for shunting inhibitory cellular neural networks with-out global Lipschitz activation functions [J]. Journal of Computational and Applied Mathematics,2007,203:159-168.
5. Liu B, Huang L. Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays[J]. Chaos, Solitons and Fractals,2007,31:211-217.
6. Liu Y, You Z, Cao L. Almost periodic solution of shunting inhibitory cellular neural networks with time-varying and continuously distributed delays[J]. Physics Letters A, 2007,364:17-28.
7. Zhao W, Zhang H. On almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients and time-varying delays[J]. Nonlinear Analysis: Real World Applications,2008,9:2326-2336.
8. Ding H, Liang J, Xiao T. Existence of almost periodic solutions for SICNNs with time-varying delays[J]. Physics Letters A,2008,372:5411-5416.
9. Cai M, Zhang H, Yuan Z. Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays[J]. Mathematics and Computers in Simulation,2008,78:548-558.
10. Chen L, Zhao H. Global stability of almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients [J]. Chaos, Solitons and Fractals, 2008,35:351-357.
11. Shao J, Wang L, Ou C. Almost periodic solutions for shunting inhibitory cellular neural networks without global Lipschitz activaty functions[J]. Applied Mathemati-cal Modelling,2009,33:2575-2581.
12. Fink A. Almost periodic differential equations[M]. Berlin:Springer,1974.
13. Zhou L, Hu G. Global exponential periodicity and stability of cellular neural networks with variable and distributed delays [J]. Applied Mathematics and Computation,2008, 195:402-411.
14. Li T, Fei S. Stability analysis of Cohen-Grossberg neural networks with time-varying and distributed delays[J]. Neurocomputing,2008,71:1069-1081.
15. Zhang Q, Wei X, Xu J. Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays[J]. Chaos, Solitons and Fractals,2008,36:985-990.
16. Zhao W. Dynamics of Cohen-Grossberg neural network with variable coefficients and time-varying delays[J]. Nonlinear Analysis:Real World Applications,2008,9:1024-1037.
17. Xiong W, Zhou Q, Xiao B, Yu Y. Global exponential stability of cellular neural net-works with mixed delays and impulses[J]. Chaos, Solitons and Fractals,2007,34: 896-902.
18. Huang Z, Yang Q, Luo X. Exponential stability of impulsive neural networks with time-varying delays[J]. Chaos, Solitons and Fractals,2008,35:770-780.
19. Long S, Xu D. Delay-dependent stability analysis for impulsive neural networks with time-varying delays[J]. Neurocomputing,2008,71:1705-1713.
20. Wu H, Xue X. Stability analysis for neural networks with inverse Lipschitzian neuron activations and impulses[J]. Applied Mathematical Modelling,2008,32:2347-2359.
21. Song Q, Zhang J. Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays[J]. Nonlinear Analysis:Real World Applications, 2008,9:500-510.
22. Ahmada S, Stamov I. Global exponential stability for impulsive cellular neural net- works with time-varying delays[J]. Nonlinear Analysis,2008,69:786-795.
23. Tan M, Zhang Y. New sufficient conditions for global asymptotic stability of Cohen-Grossberg neural networks with time-varying delays[J]. Nonlinear Analysis:Real World Applications,2009,10:2139-2145.
24. Liu K, Zhang H. An improved global exponential stability criterion for delayed neural networks[J]. Nonlinear Analysis:Real World Applications,2009,10:2613-2619.
25. Wang Y. Global exponential stability analysis of bidirectional associative memory neural networks with time-varying delays[J]. Nonlinear Analysis:Real World Ap-plications,2009,10:1527-1539.
26. Idels L, Kipnis M. Stability criteria for a nonlinear nonautonomous system with de-lays[J]. Applied Mathematical Modelling,2009,33:2293-2297.
27. Wang J, Huang L, Guo Z. Dynamical behavior of delayed Hopfield neural networks with discontinuous activations [J]. Applied Mathematical Modelling,2009,33:1793-1802.
28. Li T, Guo L, Lin C, Sun C. New results on global asymptotic stability analysis for neural networks with time-varying delays [J]. Nonlinear Analysis:Real World Appli-cations,2009,10:554-562.
29. Kwon O, Park J. Improved delay-dependent stability criterion for neural networks with time-varying delays[J]. Physics Letters A,2009,373:529-535.
30. Souza F, Palhares R, Ekel P. Improved asymptotic stability analysis for uncertain de-layed state neural networks[J]. Chaos, Solitons and Fractals,2009,39:240-247.
31. Sun J, Liu G, Chen J, Rees D. Improved stability criteria for neural networks with time-varying delay[J]. Physics Letters A,2009,373:342-348.
32. Qiu F, Cui B, Wu W. Global exponential stability of high order recurrent neural net-work with time-varying delays[J]. Applied Mathematical Modelling,2009,33:198-210.
33. Liu B. Stability of shunting inhibitory cellular neural networks with unbounded time-varying delays[J]. Applied Mathematics Letters,2009,22:1-5.
34. Zhao H, Mao Z. Boundedness and stability of nonautonomous cellular neural networks with reaction-diffusion terms [J]. Mathematics and Computers in Simulation,2009,79: 1603-1617.
35. Yang D, Liao X, Hu C, Wang Y. New delay-dependent exponential stability criteria of BAM. neural networks with time delays [J]. Mathematics and Computers in Simulation, 2009,79:1679-1697.
36. Liu Z, Zhang H, Wang Z. Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays[J]. Neurocomputing,2009,72:1056-1064.
37. Chen Y, Wu Y. Novel delay-dependent stability criteria of neural networks with time-varying delay[J]. Neurocomputing,2009,72:1065-1070.
38. Li C, Feng G. Delay-interval-dependent stability of recurrent neural networks with time-varying delay [J]. Neurocomputing,2009,72:1179-1183.
39. Zhang B, Xu S, Zou Y. Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks withtime-varying delays [J]. Neurocomputing, 2008,72:321-330.
40. Yang D, Liao X, Chen Y, Guo S, Wang H. New delay-dependent global asymptotic stability criteria of delayed Hopfield neural networks [J]. Nonlinear Analysis:Real World Applications,2008,9:1894-1904.
41. Liao X, Yang J, Guo S. Exponential stability of Cohen-Grossberg neural networks with delays[J]. Communications in Nonlinear Science and Numerical Simulation,2008,13: 1767-1775.
42. Zhou Q, Wan L. Impulsive effects on stability of Cohen-Grossberg-type bidirectional associative memory neural networks with delays[J]. Nonlinear Analysis:Real World Applications,2009,10:2531-2540.
43. Li Z, Li K. Stability analysis of impulsive Cohen-Grossberg neural networks with distributed delays and reaction-diffusion terms [J]. Applied Mathematical Modelling, 2009,33:1337-1348.
44. Zhou J, Li S. Global exponential stability of impulsive BAM neural networks with distributed delays[J]. Neurocomputing,2009,72:1688-1693.
45. Zhou Q. Global exponential stability of BAM neural networks with distributed delays and impulses[J]. Nonlinear Analysis:Real World Applications,2009,10:144-153.
46. Xia Y, Wong P. Global exponential stability of a class of retarded impulsive differential equations with applications[J]. Chaos, Solitons and Fractals,2009,39:440-453.
47. Li D, Yang D, Wang H, Zhang X, Wan S. Asymptotical stability of multi-delayed cellular neural networks with impulsive effects[J]. Physica A,2009,388:218-224.
48. Li K, Song Q. Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms[J]. Neurocomputing,2008,72: 231-240.
49. Xia Y, Huang Z, Han M. Exponential p-stability of delayed Cohen-Grossberg-type BAM neural networks with impulses[J]. Chaos, Solitons and Fractals,2008,38:806-818.
50. Chen J, Cui B. Impulsive effects on global asymptotic stability of delay BAM neural networks[J]. Chaos, Solitons and Fractals,2008,38:1115-1125.
51. Zhou J, Li S, Yang Z. Global exponential stability of Hopfield neural networks with distributed delays[J]. Applied Mathematical Modelling,2009,33:1513-1520.
52. Chen S, Zhao W, Xu Y. New criteria for globally exponential stability of delayed Cohen-Grossberg neural network[J]. Mathematics and Computers in Simulation, 2009,79:1527-1543.
53. Wang Z, Liu Y, Liu X. State estimation for jumping recurrent neural networks with discrete and distributed delays[J]. Neural Networks,2009,22:41-48.
54. Cui B, Wu W. Global exponential stability of Cohen-Grossberg neural networks with distributed delays[J]. Neurocomputing,2008,72:386-391.
55. Li T, Luo Q, Sun C, Zhang B. Exponential stability of recurrent neural networks with time-varying discrete and distributed delays[J]. Nonlinear Analysis:Real World Ap-plications,2009,10:2581-2589.
56. Li T, Fei S, Guo Y, Zhu Q. Stability analysis on Cohen-Grossberg neural networks with both time-varying and continuously distributed delays[J]. Nonlinear Analysis: Real World Applications,2009,10:2600-2612.
57. Fang S, Jiang M, Wang X. Exponential convergence estimates for neural networks with discrete and distributed delays[J]. Nonlinear Analysis:Real World Applications, 2009,10:702-714.
58. Zhou Y, Zhong S, Ye M, Shi Z. Global asymptotic stability analysis of nonlinear dif-ferential equations in hybrid bidirectional associative memory neural network swith distributed time-varying delays[J]. Neurocomputing,2009,72:1803-1807.
59. Yu J, Zhang K, Fei S, Li T. Simplified exponential stability analysis for recurrent neural networks with discrete and distributed time-varying delays[J]. Applied Mathematics and Computation,2008,205:465-474.
60. Wu H, Shan C. Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses [J]. Applied Mathematical Modelling, 2009,33:2564-2574.
61. Wu A, Fu C. Exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying and distributed delays [J]. European Journal of Pure and Applied Mathematics,2009,2(3):448-461.
62. Fu C, Wu A. Global exponential stability of reaction-diffusion delayed BAM neural networks with Dirichlet boundary conditions[J]. Lecture Notes in Computer Science, 2009,5551:303-312.
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