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Bogdanov‐Takens and Triple Zero Bifurcations of a Delayed Modified Leslie‐Gower Predator Prey System

Author

Listed:
  • Xia Liu
  • Jinling Wang

Abstract

A delayed modified Leslie‐Gower predator prey system with nonlinear harvesting is considered. The existence conditions that an equilibrium is Bogdanov‐Takens (BT) or triple zero singularity of the system are given. By using the center manifold reduction, the normal form theory, and the formulae developed by Xu and Huang, 2008 and Qiao et al., 2010, the normal forms and the versal unfoldings for this singularity are presented. The Hopf bifurcation of the system at another interior equilibrium is analyzed by taking delay (small or large) as bifurcation parameter.

Suggested Citation

  • Xia Liu & Jinling Wang, 2013. "Bogdanov‐Takens and Triple Zero Bifurcations of a Delayed Modified Leslie‐Gower Predator Prey System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:605471
    DOI: 10.1155/2013/605471
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    References listed on IDEAS

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    1. Li, Yilong & Xiao, Dongmei, 2007. "Bifurcations of a predator–prey system of Holling and Leslie types," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 606-620.
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