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Asymptotic Stability of Impulsive Cellular Neural Networks with Infinite Delays via Fixed Point Theory

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  • Yutian Zhang
  • Yuanhong Guan

Abstract

We employ the new method of fixed point theory to study the stability of a class of impulsive cellular neural networks with infinite delays. Some novel and concise sufficient conditions are presented ensuring the existence and uniqueness of solution and the asymptotic stability of trivial equilibrium at the same time. These conditions are easily checked and do not require the boundedness and differentiability of delays.

Suggested Citation

  • Yutian Zhang & Yuanhong Guan, 2013. "Asymptotic Stability of Impulsive Cellular Neural Networks with Infinite Delays via Fixed Point Theory," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:427827
    DOI: 10.1155/2013/427827
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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.
    2. Li, Kelin & Zhang, Xinhua & Li, Zuoan, 2009. "Global exponential stability of impulsive cellular neural networks with time-varying and distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1427-1434.
    3. Zhang, Yutian & Luo, Qi, 2012. "Novel stability criteria for impulsive delayed reaction–diffusion Cohen–Grossberg neural networks via Hardy–Poincarè inequality," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1033-1040.
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