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Global existence of periodic solutions in a special neural network model with two delays

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  • Dong, Ying
  • Sun, Chengjun

Abstract

A simple neural network model with two delays is considered. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when the sum of two delays passes through a sequence of critical values. Using a global Hopf bifurcation theorem for FDE due to Wu [Wu J. Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 1998;350:4799–838], a group of sufficient conditions for this model to have multiple periodic solutions are obtained when the sum of delays is sufficiently large. Numerical simulations are presented to support the obtained theoretical results.

Suggested Citation

  • Dong, Ying & Sun, Chengjun, 2009. "Global existence of periodic solutions in a special neural network model with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2249-2257.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2249-2257
    DOI: 10.1016/j.chaos.2007.06.106
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    References listed on IDEAS

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    1. Park, Ju H., 2006. "A novel criterion for global asymptotic stability of BAM neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 446-453.
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    5. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
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