Dynamic Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

Stochastic effects on convergence dynamics of reaction-diffusion Cohen-Grossberg neural networks (CGNNs) with delays are studied. By utilizing Poincaré inequality, constructing suitable Lyapunov functionals, and employing the method of stochastic analysis and nonnegative semimartingale convergence theorem, some sufficient conditions ensuring almost sure exponential stability and mean square exponential stability are derived. Diffusion term has played an important role in the sufficient conditions, which is a preeminent feature that distinguishes the present research from the previous. Two numerical examples and comparison are given to illustrate our results.

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

[2]  D. Williams.  STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[3]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  R. Temam.  Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .

[5]  John Guckenheimer,et al.  Review: Roger Temam, Infinite-dimensional dynamical systems in mechanics and physics , 1989 .

[6]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[7]  R. Peña-Sierra,et al.  ABOUT KINKS IN AlGaAs LASERS LIGHT-CURRENT CHARACTERISTIC , 2001 .

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

[9]  J. Buhmann,et al.  Influence of noise on the function of a “physiological” neural network , 1987, Biological Cybernetics.

[10]  Kwok-Wo Wong,et al.  Criteria for exponential stability of Cohen-Grossberg neural networks , 2004, Neural Networks.

[11]  Jianhua Sun,et al.  Mean square exponential stability of stochastic delayed Hopfield neural networks , 2005 .

[12]  Jianhua Sun,et al.  Convergence Dynamics of Stochastic Reaction-diffusion Recurrent Neural Networks with Delays , 2005, Int. J. Bifurc. Chaos.

[13]  S. Arik,et al.  Global stability analysis of Cohen–Grossberg neural networks with time varying delays , 2005 .

[14]  T. Elston,et al.  Stochasticity in gene expression: from theories to phenotypes , 2005, Nature Reviews Genetics.

[15]  Q. Song,et al.  Global dissipativity of neural networks with both variable and unbounded delays , 2005 .

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

[17]  J. Ruan,et al.  Global stability analysis of impulsive Cohen–Grossberg neural networks with delay , 2005 .

[18]  Nan Ding,et al.  Dynamic analysis of stochastic Cohen-Grossberg neural networks with time delays , 2006, Appl. Math. Comput..

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

[20]  Qiankun Song,et al.  Global exponential robust stability of Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms , 2006, J. Frankl. Inst..

[21]  Kunlun Wang,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with delays and reaction-diffusion terms , 2006, Neurocomputing.

[22]  Jinde Cao,et al.  Stability of Cohen-Grossberg neural networks with time-varying delays , 2007, Neural Networks.

[23]  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.

[24]  Qinghua Zhou,et al.  Mean Value Exponential Stability of Stochastic Reaction-diffusion Generalized Cohen-grossberg Neural Networks with Time-Varying Delay , 2007, Int. J. Bifurc. Chaos.

[25]  Nan Ding,et al.  Dynamic analysis of stochastic bidirectional associative memory neural networks with delays , 2007 .

[26]  Jinde Cao,et al.  Exponential Stability for Impulsive BAM Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms , 2007 .

[27]  Chuandong Li,et al.  Stability of Cohen-Grossberg neural networks with unbounded distributed delays , 2007 .

[28]  J. Ruan,et al.  Global dynamic analysis of general Cohen–Grossberg neural networks with impulse , 2007 .

[29]  G. Feng,et al.  Delay-dependent stability for uncertain stochastic neural networks with time-varying delay , 2007 .

[30]  Yonghui Sun,et al.  pth moment exponential stability of stochastic recurrent neural networks with time-varying delays , 2007 .

[31]  Jianhua Sun,et al.  Exponential stability of reaction–diffusion generalized Cohen–Grossberg neural networks with time-varying delays , 2007 .

[32]  Li Wan,et al.  Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays , 2007 .

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

[34]  Qinghua Zhou,et al.  Global Exponential Stability for a Class of impulsive integro-Differential equation , 2008, Int. J. Bifurc. Chaos.

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

[36]  Shouming Zhong,et al.  Mean square stability analysis of impulsive stochastic differential equations with delays , 2008 .

[37]  Zidong Wang,et al.  Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays , 2008 .

[38]  Jianhua Sun,et al.  Convergence dynamics of stochastic reaction–diffusion recurrent neural networks with continuously distributed delays☆ , 2008 .

[39]  Pagavathigounder Balasubramaniam,et al.  Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays , 2008, Appl. Math. Comput..

[40]  Linshan Wang,et al.  Stochastic exponential stability of the delayed reaction–diffusion recurrent neural networks with Markovian jumping parameters , 2008 .

[41]  Lihong Huang,et al.  Convergence dynamics of Cohen-Grossberg neural networks with continuously distributed delays , 2008, Appl. Math. Comput..

[42]  Ju H. Park,et al.  LMI optimization approach on stability for delayed neural networks of neutral-type , 2008, Appl. Math. Comput..

[43]  Chuangxia Huang,et al.  Mean square exponential stability of stochastic recurrent neural networks with time-varying delays , 2008, Comput. Math. Appl..

[44]  Xinzhi Liu,et al.  Impulsive Stabilization of High-Order Hopfield-Type Neural Networks With Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[45]  Wu‐Hua Chen,et al.  Mean square exponential stability of uncertain stochastic delayed neural networks , 2008 .

[46]  Jian-an Fang,et al.  Global stability of stochastic high-order neural networks with discrete and distributed delays , 2008 .

[47]  Hongyong Zhao,et al.  Almost sure exponential stability of stochastic fuzzy cellular neural networks with delays , 2009 .

[48]  Bao Shi,et al.  Global exponential stability of Cohen-Grossberg neural networks with variable delays , 2009 .

[49]  Jinxian Li,et al.  Dynamical analysis of Cohen-Grossberg neural networks with time-delays and impulses , 2009, Neurocomputing.

[50]  Li Yang,et al.  Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays , 2009 .

[51]  Ju H. Park,et al.  SYNCHRONIZATION OF NEURAL NETWORKS OF NEUTRAL TYPE WITH STOCHASTIC PERTURBATION , 2009 .

[52]  Yunong Zhang,et al.  New sufficient conditions for global asymptotic stability of Cohen–Grossberg neural networks with time-varying delays , 2009 .

[53]  Xiaodi Li,et al.  Exponential stability of Cohen-Grossberg-type BAM neural networks with time-varying delays via impulsive control , 2009, Neurocomputing.

[54]  François Fages,et al.  Dynamics of the interlocked positive feedback loops explaining the robust epigenetic switching in Candida albicans. , 2009, Journal of theoretical biology.

[55]  Baotong Cui,et al.  Robust exponential stability of interval Cohen-Grossberg neural networks with time-varying delays , 2009 .

[56]  Ju H. Park,et al.  DELAY-DEPENDENT STABILITY CRITERION FOR BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH INTERVAL TIME-VARYING DELAYS , 2009 .

[57]  Huaguang Zhang,et al.  Dynamics analysis of impulsive stochastic Cohen-Grossberg neural networks with Markovian jumping and mixed time delays , 2009, Neurocomputing.

[58]  Jun-Guo Lu,et al.  Global exponential stability of impulsive Cohen–Grossberg neural networks with continuously distributed delays , 2009 .

[59]  Jinde Cao,et al.  On pth moment exponential stability of stochastic Cohen-Grossberg neural networks with time-varying delays , 2010, Neurocomputing.

[60]  Jinde Cao,et al.  Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).