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The Effect of Time Delay on Dynamical Behavior in an Ecoepidemiological Model

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  • Changjin Xu
  • Yusen Wu

Abstract

A delayed predator‐prey model with disease in the prey is investigated. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. The effect of the two different time delays on the dynamical behavior has been given. Numerical simulations are performed to illustrate the theoretical analysis. Finally, the main conclusions are drawn.

Suggested Citation

  • Changjin Xu & Yusen Wu, 2012. "The Effect of Time Delay on Dynamical Behavior in an Ecoepidemiological Model," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:286961
    DOI: 10.1155/2012/286961
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    References listed on IDEAS

    as
    1. Li, Kai & Wei, Junjie, 2009. "Stability and Hopf bifurcation analysis of a prey–predator system with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2606-2613.
    2. Xu, Rui & Ma, Zhien, 2008. "Stability and Hopf bifurcation in a ratio-dependent predator–prey system with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 669-684.
    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, John Wiley & Sons, vol. 2009(1).
    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, Hindawi, vol. 2009, pages 1-18, November.
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