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Stability and Global Hopf Bifurcation Analysis on a Ratio‐Dependent Predator‐Prey Model with Two Time Delays

Author

Listed:
  • Huitao Zhao
  • Yiping Lin
  • Yunxian Dai

Abstract

A ratio‐dependent predator‐prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998) for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.

Suggested Citation

  • Huitao Zhao & Yiping Lin & Yunxian Dai, 2013. "Stability and Global Hopf Bifurcation Analysis on a Ratio‐Dependent Predator‐Prey Model with Two Time Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:321930
    DOI: 10.1155/2013/321930
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    References listed on IDEAS

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    1. Zheng, Baodong & Zhang, Yazhuo & Zhang, Chunrui, 2008. "Global existence of periodic solutions on a simplified BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1397-1408.
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