Global dynamics for non-autonomous reaction-diffusion neural networks with time-varying delays

In this paper, a class of non-autonomous reaction-diffusion neural networks with time-varying delays is considered. Novel methods to study the global dynamical behavior of these systems are proposed. Employing the properties of diffusion operator and the method of delayed inequalities analysis, we investigate global exponential stability, positive invariant sets and global attracting sets of the neural networks under consideration. Furthermore, conditions sufficient for the existence and uniqueness of periodic attractors for periodic neural networks are derived and the existence range of the attractors is estimated. Finally two examples are given to demonstrate the effectiveness of these results.

[1]  Zhigang Zeng,et al.  Improved conditions for global exponential stability of recurrent neural networks with time-varying delays , 2006, IEEE Transactions on Neural Networks.

[2]  E. Zeidler.  Nonlinear functional analysis and its applications , 1988 .

[3]  Daoyi Xu,et al.  Invariant and attracting sets of Hopfield neural networks with delay , 2001 .

[4]  Lishan Kang,et al.  Existence and stability of global solution for generalized Hopfield neural network system , 1994, Neural Parallel Sci. Comput..

[5]  Qiang Zhang,et al.  Delay-dependent exponential stability of cellular neural networks with time-varying delays , 2005 .

[6]  Zhang Yrt.  Global exponential stability and periodic solutions of delay Hopfield neural networks , 1996 .

[7]  Daoyi Xu,et al.  Global dynamics of Hopfield neural networks involving variable delays , 2001 .

[8]  Teng Zhi-dong.  Boundedness and stability for nonautonomous cellular neural networks with delay , 2006 .

[9]  Jinde Cao,et al.  Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays , 2004 .

[10]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[11]  Shuzi Yang,et al.  Stability of general neural networks with reaction-diffusion , 2007, Science in China Series : Information Sciences.

[12]  Dao-Yi Xu,et al.  Invariant and attracting sets of Hopfield neural networks with delay , 2001, Int. J. Syst. Sci..

[13]  Zhao Xin-quan.  Stability of Hopfield Neural Networks with Reaction-diffusion Terms , 2000 .

[14]  Nonlinear functional analysis and its applications, part I: Fixed-point theorems , 1991 .

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

[16]  Zhang Yi,et al.  Global exponential stability and periodic solutions of delay Hopfield neural networks , 1996, Int. J. Syst. Sci..

[17]  Jianhong Wu.  Theory and Applications of Partial Functional Differential Equations , 1996 .

[18]  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.

[19]  Huiyan Zhu,et al.  Global stability of cellular neural networks with constant and variable delays , 2003 .

[20]  Korris Fu-Lai Chung,et al.  Absolute exponential stability of a class of recurrent neural networks with multiple and variable delays , 2005, Theor. Comput. Sci..

[21]  Zhigang Zeng,et al.  Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli , 2006, Neural Networks.

[22]  Zhang Yi,et al.  Global exponential convergence of recurrent neural networks with variable delays , 2004, Theor. Comput. Sci..

[23]  Pauline van den Driessche,et al.  Global Attractivity in Delayed Hopfield Neural Network Models , 1998, SIAM J. Appl. Math..