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Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays

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  • Kaiyu Liu
  • Zhengqiu Zhang
  • Liping Wang

Abstract

We investigate first the existence of periodic solution in general Cohen-Grossberg BAM neural networks with multiple time-varying delays by means of using degree theory. Then using the existence result of periodic solution and constructing a Lyapunov functional, we discuss global exponential stability of periodic solution for the above neural networks. Our result on global exponential stability of periodic solution is different from the existing results. In our result, the hypothesis for monotonicity ineqiality conditions in the works of Xia (2010) Chen and Cao (2007) on the behaved functions is removed and the assumption for boundedness in the works of Zhang et al. (2011) and Li et al. (2009) is also removed. We just require that the behaved functions satisfy sign conditions and activation functions are globally Lipschitz continuous.

Suggested Citation

  • Kaiyu Liu & Zhengqiu Zhang & Liping Wang, 2012. "Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-21, May.
    • Handle: RePEc:hin:jnlaaa:805846
    DOI: 10.1155/2012/805846
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    Cited by:

    1. Zhang, Qunjiao, 2014. "Robust synchronization of FitzHugh–Nagumo network with parameter disturbances by sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 22-26.
    2. Gani Stamov & Ivanka Stamova & Stanislav Simeonov & Ivan Torlakov, 2020. "On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays," Mathematics, MDPI, vol. 8(3), pages 1-14, March.

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