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Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay

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  • Liu, Xiaoming
  • Liao, Xiaofeng

Abstract

In this paper, we consider the delayed differential equations modeling three-neuron equations with only a time delay. Using the time delay as a bifurcation parameter, necessary and sufficient conditions for Hopf bifurcation to occur are derived. Numerical results indicate that for this model, Hopf bifurcation is likely to occur at suitable delay parameter values.

Suggested Citation

  • Liu, Xiaoming & Liao, Xiaofeng, 2009. "Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 481-490.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:481-490
    DOI: 10.1016/j.chaos.2007.07.096
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    References listed on IDEAS

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    1. Liao, Xiaofeng & Chen, Guanrong, 2005. "Hopf bifurcation and chaos analysis of Chen’s system with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 197-220.
    2. Liao, Xiaofeng & Li, Chuandong & Zhou, Shangbo, 2005. "Hopf bifurcation and chaos in macroeconomic models with policy lag," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 91-108.
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    Cited by:

    1. Jana, Soovoojeet & Kar, T.K., 2013. "Modeling and analysis of a prey–predator system with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 42-53.

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