The stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms

The global asymptotic stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms is investigated. Under some suitable assumptions and using Lyapunov–Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.

[1]  Chuandong Li,et al.  Stability of delayed memristive neural networks with time-varying impulses , 2014, Cognitive Neurodynamics.

[2]  João Pedro Hespanha,et al.  Lyapunov conditions for input-to-state stability of impulsive systems , 2008, Autom..

[3]  Richard E. Mortensen,et al.  Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam) , 1991, SIAM Rev..

[4]  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.

[5]  Qi Luo,et al.  Global exponential stability of impulsive delayed reaction-diffusion neural networks via Hardy-Poincarè inequality , 2012, Neurocomputing.

[6]  Xiaodi Li,et al.  Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays , 2011, Appl. Math. Comput..

[7]  Zuoan Li,et al.  Stability analysis of impulsive Cohen-Grossberg neural networks with distributed delays and reaction-diffusion terms , 2009 .

[8]  Xinhua Zhang,et al.  Delay-dependent exponential stability for impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms , 2011 .

[9]  Hongbin Zhang,et al.  Global exponential stability of impulsive fuzzy Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms , 2012, Neurocomputing.

[10]  Kelin Li,et al.  Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms , 2009 .

[11]  Shouming Zhong,et al.  Dynamical behaviors of impulsive reaction-diffusion Cohen-Grossberg neural network with delays , 2010, Neurocomputing.

[12]  Tingwen Huang,et al.  Exponential input-to-state stability of recurrent neural networks with multiple time-varying delays , 2013, Cognitive Neurodynamics.

[13]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[14]  Xiaodi Li,et al.  New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays , 2010 .

[15]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[16]  Xiaodi Li,et al.  LMI Approach for Stationary Oscillation of Interval Neural Networks With Discrete and Distributed Time-Varying Delays Under Impulsive Perturbations , 2010, IEEE Transactions on Neural Networks.

[17]  Peng Shi,et al.  Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[18]  Kelin Li,et al.  Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms , 2008, Neurocomputing.

[19]  Junmi Li,et al.  Dynamical Behaviors of Impulsive Stochastic Reaction-Diffusion Neural Networks with Mixed Time Delays , 2012 .

[20]  Xinzhi Liu,et al.  Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays , 2010, Math. Comput. Model..

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

[22]  Chun Yin,et al.  On the Dynamics of an Impulsive Reaction-Diffusion Predator-Prey System with Ratio-Dependent Functional Response , 2011 .

[23]  Junping Shi,et al.  Stability of impulsive stochastic differential delay systems and its application to impulsive stocha , 2011 .

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

[25]  Rui Xu,et al.  Global asymptotic stability of stochastic reaction–diffusion neural networks with time delays in the leakage terms ☆ , 2012 .

[26]  Danhua He,et al.  Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks with delays , 2012, Math. Comput. Simul..

[27]  Daoyi Xu,et al.  Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms , 2009 .

[28]  Xiaodi Li,et al.  LMI conditions for stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays☆ , 2011 .

[29]  Bing Li,et al.  Existence and exponential stability of periodic solution for impulsive Cohen-Grossberg neural networks with time-varying delays , 2012, Appl. Math. Comput..

[30]  Jinde Cao,et al.  Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays , 2014, Cognitive Neurodynamics.

[31]  Y. Wang,et al.  Stability Analysis of Markovian Jumping Stochastic Cohen–Grossberg Neural Networks With Mixed Time Delays , 2008, IEEE Transactions on Neural Networks.

[32]  Huaguang Zhang,et al.  Global Asymptotic Stability of Reaction–Diffusion Cohen–Grossberg Neural Networks With Continuously Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[33]  Xiaodi Li,et al.  Impulsive Control for Existence, Uniqueness, and Global Stability of Periodic Solutions of Recurrent Neural Networks With Discrete and Continuously Distributed Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[34]  R. Rakkiyappan,et al.  Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations , 2010 .

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

[36]  S. Taylor.  DIFFUSION PROCESSES AND THEIR SAMPLE PATHS , 1967 .

[37]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.