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Stability and Hopf Bifurcation Analysis on a Bazykin Model with Delay

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  • Jianming Zhang
  • Lijun Zhang
  • Chaudry Masood Khalique

Abstract

The dynamics of a prey-predator system with a finite delay is investigated. We show that a sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases. By using the theory of normal form and center manifold, explicit expressions for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.

Suggested Citation

  • Jianming Zhang & Lijun Zhang & Chaudry Masood Khalique, 2014. "Stability and Hopf Bifurcation Analysis on a Bazykin Model with Delay," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnlaaa:539684
    DOI: 10.1155/2014/539684
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    Cited by:

    1. Zhang, Bei & Xia, Yonghui & Zhu, Wenjing & Bai, Yuzhen, 2019. "Explicit exact traveling wave solutions and bifurcations of the generalized combined double sinh–cosh-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    2. Jianming Zhang & Lijun Zhang & Yuzhen Bai, 2019. "Stability and Bifurcation Analysis on a Predator–Prey System with the Weak Allee Effect," Mathematics, MDPI, vol. 7(5), pages 1-15, May.

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