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Periodic oscillatory solution in delayed competitive–cooperative neural networks: A decomposition approach

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  • Yuan, Kun
  • Cao, Jinde

Abstract

In this paper, the problems of exponential convergence and the exponential stability of the periodic solution for a general class of non-autonomous competitive–cooperative neural networks are analyzed via the decomposition approach. The idea is to divide the connection weights into inhibitory or excitatory types and thereby to embed a competitive–cooperative delayed neural network into an augmented cooperative delay system through a symmetric transformation. Some simple necessary and sufficient conditions are derived to ensure the componentwise exponential convergence and the exponential stability of the periodic solution of the considered neural networks. These results generalize and improve the previous works, and they are easy to check and apply in practice.

Suggested Citation

  • Yuan, Kun & Cao, Jinde, 2006. "Periodic oscillatory solution in delayed competitive–cooperative neural networks: A decomposition approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 223-231.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:1:p:223-231
    DOI: 10.1016/j.chaos.2005.04.016
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    1. Cao, Jinde & Ho, Daniel W.C., 2005. "A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1317-1329.
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    Cited by:

    1. Mak, K.L. & Peng, J.G. & Xu, Z.B. & Yiu, K.F.C., 2007. "A new stability criterion for discrete-time neural networks: Nonlinear spectral radius," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 424-436.
    2. Gui, Zhanji & Ge, Weigao, 2007. "Periodic solutions of nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1760-1771.
    3. Sun, Jitao & Wang, Qing-Guo & Gao, Hanqiao, 2009. "Periodic solution for nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1423-1427.

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