Mean square exponential stability of stochastic neural networks with reaction-diffusion terms and delays

Abstract In this paper, some sufficient conditions ensuring mean square exponential stability of the equilibrium point of a class of stochastic neural networks with reaction–diffusion terms and time-varying delays are obtained. The conditions involving the effect of diffusion terms reduce the conservatism of the previous results. Finally, we give a numerical example to verify the effectiveness of our results.

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

[2]  Shuping Bao,et al.  Exponential stability of reaction-diffusion Cohen-Grossberg neural networks with variable coefficients and distributed delays , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[3]  Bing Li,et al.  Mean square asymptotic behavior of stochastic neural networks with infinitely distributed delays , 2009, Neurocomputing.

[4]  Junguo Lu.  Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

[5]  Qinghua Zhou,et al.  Exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays , 2008, Appl. Math. Comput..

[6]  Stability in mean of partial variables for stochastic reaction diffusion systems , 2009 .

[7]  Chuandong Li,et al.  A global exponential robust stability criterion for interval delayed neural networks with variable delays , 2006, Neurocomputing.

[8]  Jingjing Liu,et al.  Existence of three solutions for a class of quasilinear elliptic systems involving the (p(x), q(x))-Laplacian , 2009 .

[9]  Walter Allegretto,et al.  Stability for delayed reaction–diffusion neural networks , 2007 .

[10]  Linshan Wang,et al.  Global exponential robust stability of reaction¿diffusion interval neural networks with time-varying delays , 2006 .

[11]  Qinghua Zhou,et al.  Exponential stability of stochastic delayed Hopfield neural networks , 2008, Appl. Math. Comput..

[12]  L. Chua.  Cnn: A Paradigm for Complexity , 1998 .

[13]  L. Pandolfi,et al.  On stability of cellular neural networks with delay , 1993 .

[14]  Vedat Tavsanoglu,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays , 2005, Neurocomputing.

[15]  Jiye Zhang,et al.  Global exponential stability of Cohen–Grossberg neural networks with variable delays☆ , 2005 .