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Stability and bifurcation analysis in a basic model of the immune response with delays

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  • Yu, Chunbo
  • Wei, Junjie

Abstract

The dynamics of the Mayer model with delays has been studied. Firstly, the linear stabilities with one delay and two delays are investigated, respectively. It is found that there are stability switches for time delays, and Hopf bifurcations when time delays cross through some critical values. Then, using the normal form method and the center manifold theorem, the direction and stability of the Hopf bifurcations are determined. Finally, some numerical simulations are carried out to illustrate the results.

Suggested Citation

  • Yu, Chunbo & Wei, Junjie, 2009. "Stability and bifurcation analysis in a basic model of the immune response with delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1223-1234.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1223-1234
    DOI: 10.1016/j.chaos.2008.05.007
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    References listed on IDEAS

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    1. Jiang, Zhichao & Wei, Junjie, 2008. "Stability and bifurcation analysis in a delayed SIR model," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 609-619.
    2. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
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    Cited by:

    1. Changjin Xu, 2017. "Delay-Induced Oscillations in a Competitor-Competitor-Mutualist Lotka-Volterra Model," Complexity, Hindawi, vol. 2017, pages 1-12, April.

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