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Stability and Bifurcation in a Delayed Holling-Tanner Predator-Prey System with Ratio-Dependent Functional Response

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  • Juan Liu
  • Zizhen Zhang
  • Ming Fu

Abstract

We analyze a delayed Holling-Tanner predator-prey system with ratio-dependent functional response. The local asymptotic stability and the existence of the Hopf bifurcation are investigated. Direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are studied by deriving the equation describing the flow on the center manifold. Finally, numerical simulations are presented for the support of our analytical findings.

Suggested Citation

  • Juan Liu & Zizhen Zhang & Ming Fu, 2012. "Stability and Bifurcation in a Delayed Holling-Tanner Predator-Prey System with Ratio-Dependent Functional Response," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, December.
    • Handle: RePEc:hin:jnljam:384293
    DOI: 10.1155/2012/384293
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