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

Author

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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, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:805846
    DOI: 10.1155/2012/805846
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    References listed on IDEAS

    as
    1. Changjin Xu & Xiaofei He, 2011. "Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-21, June.
    2. Changjin Xu & Xiaofei He, 2011. "Stability and Bifurcation Analysis in a Class of Two‐Neuron Networks with Resonant Bilinear Terms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    3. Zixin Liu & Shu Lü & Shouming Zhong & Mao Ye, 2009. "Improved Robust Stability Criteria of Uncertain Neutral Systems with Mixed Delays," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-18, November.
    4. Zixin Liu & Shu Lü & Shouming Zhong & Mao Ye, 2009. "Improved Robust Stability Criteria of Uncertain Neutral Systems with Mixed Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
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