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Dynamical Behaviors of Impulsive Stochastic Reaction‐Diffusion Neural Networks with Mixed Time Delays

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  • Weiyuan Zhang
  • Junmin Li
  • Minglai Chen

Abstract

We discuss the dynamical behaviors of impulsive stochastic reaction‐diffusion neural networks (ISRDNNs) with mixed time delays. By using a well‐known L‐operator differential inequality with mixed time delays and combining with the Lyapunov‐Krasovkii functional approach, as well as linear matrix inequality (LMI) technique, some novel sufficient conditions are derived to ensure the existence, uniqueness, and global exponential stability of the periodic solutions for ISRDNNs with mixed time delays in the mean square sense. The obtained sufficient conditions depend on the reaction‐diffusion terms. The results of this paper are new and improve some of the previously known results. The proposed model is quite general since many factors such as noise perturbations, impulsive phenomena, and mixed time delays are considered. Finally, two numerical examples are provided to verify the usefulness of the obtained results.

Suggested Citation

  • Weiyuan Zhang & Junmin Li & Minglai Chen, 2012. "Dynamical Behaviors of Impulsive Stochastic Reaction‐Diffusion Neural Networks with Mixed Time Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:236562
    DOI: 10.1155/2012/236562
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    References listed on IDEAS

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    1. Lu, Jun Guo & Lu, Lin Ji, 2009. "Global exponential stability and periodicity of reaction–diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1538-1549.
    2. 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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