Exponential stability of impulsive neural networks with time-varying delays and reaction-diffusion terms

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive neural networks with time-varying delays and reaction-diffusion terms. By using Lyapunov functions method, some sufficient conditions ensuring global exponential stability of the networks are derived, and the estimated exponential convergence rate is also obtained. A numerical example is given at the end of this paper to demonstrate the effectiveness and applicability of the proposed criteria.

[1]  Xinzhi Liu,et al.  Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays , 2005, IEEE Trans. Neural Networks.

[2]  Zhidong Teng,et al.  Global eponential stability of cellular neural networks with time-varying coefficients and delays , 2004, Neural Networks.

[3]  Xinzhi Liu,et al.  Application of Impulsive Synchronization to Communication Security , 2003 .

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

[5]  Jinde Cao,et al.  Global synchronization in arrays of delayed neural networks with constant and delayed coupling , 2006 .

[6]  Xinzhi Liu,et al.  Uniform asymptotic stability of impulsive delay differential equations , 2001 .

[7]  C. V. Pao,et al.  Global asymptotic stability of Lotka-Volterra competition systems with diffusion and time delays , 2004 .

[8]  Jinde Cao,et al.  Global point dissipativity of neural networks with mixed time-varying delays. , 2006, Chaos.

[9]  Zhidong Teng,et al.  Boundedness and stability for nonautonomous cellular neural networks with delay , 2003 .

[10]  A. Zafer,et al.  Stability of the Zero Solution of Impulsive Differential Equations by the Lyapunov Second Method , 2000 .

[11]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[12]  Jinde Cao,et al.  Global exponential stability and periodicity of recurrent neural networks with time delays , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Jinde Cao,et al.  Exponential stability of high-order bidirectional associative memory neural networks with time delays , 2004 .

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

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

[16]  Daoyi Xu,et al.  Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays , 2003, Science in China Series F: Information Sciences.

[17]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[18]  Jinde Cao,et al.  Exponential stability of delayed bi-directional associative memory networks , 2003, Appl. Math. Comput..

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

[20]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[21]  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.

[22]  Hong Qiao,et al.  A new approach to stability of neural networks with time-varying delays , 2002, Neural Networks.

[23]  Jinde Cao,et al.  Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays , 2003 .

[24]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[25]  S. Arik.  Global asymptotic stability of a larger class of neural networks with constant time delay , 2003 .

[26]  Chien-Yu Lu,et al.  Stability of cellular neural networks with time-varying delay , 2003 .

[27]  Guanrong Chen,et al.  On delayed impulsive Hopfield neural networks , 1999, Neural Networks.

[28]  Hongyong Zhao,et al.  Exponential stability and periodic oscillatory of bi-directional associative memory neural network involving delays , 2006, Neurocomputing.

[29]  Jia Li,et al.  Stability in Gilpin-Ayala competition models with diffusion , 1997 .

[30]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.