Exponential Stability for Impulsive BAM Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.

[1]  V. Sree Hari Rao,et al.  Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones , 1999, Neural Networks.

[2]  Qiang Zhang,et al.  New stability conditions for neural networks with constant and variable delays , 2005 .

[3]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

[4]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[5]  Ivanka M. Stamova,et al.  Almost periodic solutions for impulsive neural networks with delay , 2007 .

[6]  Daoyi Xu,et al.  Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays , 2006, Appl. Math. Comput..

[7]  Daoyi Xu,et al.  Impulsive delay differential inequality and stability of neural networks , 2005 .

[8]  W. Cooper,et al.  SCIENCE IN CHINA. , 1940, Science.

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

[10]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

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

[12]  Chaolong Zhang,et al.  Global stability analysis of impulsive BAM type Cohen-Grossberg neural networks with delays , 2007, Appl. Math. Comput..

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

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

[15]  James Lam,et al.  Global exponential stability of impulsive high-order BAM neural networks with time-varying delays , 2006, Neural Networks.

[16]  Yao-tang Li,et al.  Global exponential stability analysis on impulsive BAM neural networks with distributed delays , 2006 .

[17]  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.

[18]  Shengyuan Xu,et al.  A new approach to exponential stability analysis of neural networks with time-varying delays , 2006, Neural Networks.

[19]  Yongkun Li.  Global exponential stability of BAM neural networks with delays and impulses , 2005 .

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

[21]  Ju H. Park.  A novel criterion for global asymptotic stability of BAM neural networks with time delays , 2006 .

[22]  Jinde Cao,et al.  Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays , 2006 .

[23]  Yang Shuzi,et al.  Stability of general neural networks with reaction-diffusion , 2001 .

[24]  Yu Zhang,et al.  Stability of impulsive neural networks with time delays , 2005 .

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

[26]  Jianlong Qiu,et al.  Exponential stability of impulsive neural networks with time-varying delays and reaction-diffusion terms , 2007, Neurocomputing.

[27]  Q. Song,et al.  Global exponential stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2005 .

[28]  Z. Guan,et al.  An LMI Approach to Exponential Stability Analysis of Neural Networks with Time-Varying Delay , 2005, TENCON 2005 - 2005 IEEE Region 10 Conference.

[29]  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.

[30]  X. Liao,et al.  Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays , 2003 .

[31]  Lihong Huang,et al.  Global existence of periodic solutions of BAM neural networks with variable coefficients , 2003 .

[32]  S. Mohamad.  Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks , 2001 .