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Stochastic Synchronization of Reaction‐Diffusion Neural Networks under General Impulsive Controller with Mixed Delays

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  • Xinsong Yang
  • Chuangxia Huang
  • Zhichun Yang

Abstract

This paper investigates drive‐response synchronization of a class of reaction‐diffusion neural networks with time‐varying discrete and distributed delays via general impulsive control method. Stochastic perturbations in the response system are also considered. The impulsive controller is assumed to be nonlinear and has multiple time‐varying discrete and distributed delays. Compared with existing nondelayed impulsive controller, this general impulsive controller is more practical and essentially important since time delays are unavoidable in practical operation. Based on a novel impulsive differential inequality, the properties of random variables and Lyapunov functional method, sufficient conditions guaranteeing the global exponential synchronization in mean square are derived through strict mathematical proof. In our synchronization criteria, the distributed delays in both continuous equation and impulsive controller play important role. Finally, numerical simulations are given to show the effectiveness of the theoretical results.

Suggested Citation

  • Xinsong Yang & Chuangxia Huang & Zhichun Yang, 2012. "Stochastic Synchronization of Reaction‐Diffusion Neural Networks under General Impulsive Controller with Mixed Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:603535
    DOI: 10.1155/2012/603535
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    References listed on IDEAS

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    1. Wang, Xiaohu & Xu, Daoyi, 2009. "Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2713-2721.
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    3. Cao, Jinde & Wang, Zidong & Sun, Yonghui, 2007. "Synchronization in an array of linearly stochastically coupled networks with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 718-728.
    4. Ping Zhou & Rui Ding, 2012. "Modified Function Projective Synchronization between Different Dimension Fractional‐Order Chaotic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Lu, Jun Guo, 2008. "Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 116-125.
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    Cited by:

    1. Xinsong Yang & Mengzhe Zhou & Jinde Cao, 2013. "Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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