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Stability and Hopf Bifurcation in a Prey‐Predator System with Disease in the Prey and Two Delays

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  • Juan Liu

Abstract

This paper is concerned with a prey‐predator system with disease in the prey and two delays. Local stability of the positive equilibrium of the system and existence of local Hopf bifurcation are investigated by choosing different combinations of the two delays as bifurcation parameters. For further investigation, the direction and the stability of the Hopf bifurcation are determined by using the normal form method and center manifold theorem. Finally, some numerical simulations are given to support the theoretical analysis.

Suggested Citation

  • Juan Liu, 2014. "Stability and Hopf Bifurcation in a Prey‐Predator System with Disease in the Prey and Two Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:624546
    DOI: 10.1155/2014/624546
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    References listed on IDEAS

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    1. Hu, Guang-Ping & Li, Xiao-Ling, 2012. "Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 229-237.
    2. Zizhen Zhang & Huizhong Yang & Juan Liu, 2012. "Stability and Hopf Bifurcation in a Modified Holling-Tanner Predator-Prey System with Multiple Delays," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, November.
    3. Zizhen Zhang & Huizhong Yang & Juan Liu, 2012. "Stability and Hopf Bifurcation in a Modified Holling‐Tanner Predator‐Prey System with Multiple Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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