Asymptotic behavior of discrete solutions to delayed neural networks with impulses

In this paper, we formulate and study a new class of discrete neural networks with time dependent delay and impulses. Sufficient conditions for the asymptotic stability of a unique equilibrium of the networks with Lipschitizian activation functions are established. Also when the impulsive jumps are absent the results reduce to those of non-impulsive networks.

[1]  H. Akça,et al.  Continuous-time additive Hopfield-type neural networks with impulses , 2004 .

[2]  Zidong Wang,et al.  On global asymptotic stability of neural networks with discrete and distributed delays , 2005 .

[3]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[4]  Jinde Cao,et al.  Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays , 2004, Neural Networks.

[5]  Tharam S. Dillon,et al.  Exponential stability and oscillation of Hopfield graded response neural network , 1994, IEEE Trans. Neural Networks.

[6]  D. Bainov,et al.  Impulsive Differential Equations: Periodic Solutions and Applications , 1993 .

[7]  Lansun Chen,et al.  Impulsive vaccination of sir epidemic models with nonlinear incidence rates , 2004 .

[8]  Guanrong Chen,et al.  Dynamics of periodic delayed neural networks , 2004, Neural Networks.

[9]  Morris W. Hirsch,et al.  Convergent activation dynamics in continuous time networks , 1989, Neural Networks.

[10]  Juebang Yu,et al.  Qualitative analysis of Bi‐directional Associative Memory with time delay , 1998 .

[11]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[12]  Anthony N. Michel,et al.  Analysis and synthesis of neural networks with lower block triangular interconnecting structure , 1990 .

[13]  Liang Xuebin,et al.  Global exponential stability of Hopfield-type neural network and its applications , 1995 .

[14]  Allon Guez,et al.  On the stability, storage capacity, and design of nonlinear continuous neural networks , 1988, IEEE Trans. Syst. Man Cybern..

[15]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[16]  Eric T. Funasaki,et al.  Invasion and Chaos in a Periodically Pulsed Mass-Action Chemostat , 1993 .

[17]  X. Lou,et al.  Global asymptotic stability of delay BAM neural networks with impulses , 2006 .

[18]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[19]  Chuanzhi Bai,et al.  Stability analysis of Cohen–Grossberg BAM neural networks with delays and impulses , 2008 .

[20]  Katrin Rohlf,et al.  Impulsive control of a Lotka-Volterra system , 1998 .

[21]  K. Gopalsamy,et al.  Neuronal dynamics in time varying enviroments: Continuous and discrete time models , 2000 .

[22]  Jinde Cao,et al.  Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays , 2006 .

[23]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Jinde Cao,et al.  Global exponential stability of Hopfield neural networks , 2001, Int. J. Syst. Sci..

[25]  J. Farrell,et al.  Qualitative analysis of neural networks , 1989 .

[26]  Zhang Yi,et al.  Brief communication Periodic solutions and stability of Hopfield neural networks with variable delays , 1996, Int. J. Syst. Sci..

[27]  Wolfgang Porod,et al.  Qualitative analysis and synthesis of a class of neural networks , 1988 .

[28]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Shun-ichi Amari,et al.  Stability of asymmetric Hopfield networks , 2001, IEEE Trans. Neural Networks.

[30]  Jinde Cao.  New results concerning exponential stability and periodic solutions of delayed cellular neural networks , 2003 .

[31]  Jinde Cao,et al.  Periodic solutions and exponential stability in delayed cellular neural networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Wang,et al.  Global stability and local stability of Hopfield neural networks with delays. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  B. Shulgin,et al.  Pulse vaccination strategy in the SIR epidemic model , 1998, Bulletin of mathematical biology.

[34]  Jinde Cao,et al.  Stability and periodicity in delayed cellular neural networks with impulsive effects , 2007 .

[35]  Yongkun Li,et al.  Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses , 2004 .

[36]  Zhi-Hong Guan,et al.  On impulsive autoassociative neural networks , 2000, Neural Networks.

[37]  Yuehua Yu,et al.  Global exponential stability of cellular neural networks with continuously distributed delays and impulses , 2006 .

[38]  Xianning Liu,et al.  Complex dynamics of Holling type II Lotka–Volterra predator–prey system with impulsive perturbations on the predator ☆ , 2003 .

[39]  Jun Wang,et al.  Global stability of a class of continuous-time recurrent neural networks , 2002 .

[40]  X. Liao,et al.  Stability of Hopfield-type neural networks II , 1997 .

[41]  P K Maini,et al.  Pattern formation in a generalized chemotactic model , 1998, Bulletin of mathematical biology.

[43]  Hongyong Zhao,et al.  Global asymptotic stability of Hopfield neural network involving distributed delays , 2004, Neural Networks.

[44]  G Palm,et al.  Computing with neural networks. , 1987, Science.

[45]  Yuehua Yu,et al.  Global exponential stability of cellular neural networks with mixed delays and impulses , 2007 .

[46]  K. Gopalsamy,et al.  Dynamics of a class of discete-time neural networks and their comtinuous-time counterparts , 2000 .

[47]  Xinghua Wang,et al.  The existence and global attractivity of almost periodic sequence solution of discrete-time neural networks , 2006 .

[48]  J. Cao,et al.  Periodic oscillatory solution of bidirectional associative memory networks with delays. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[49]  K. Gopalsamy,et al.  Stability of artificial neural networks with impulses , 2004, Appl. Math. Comput..