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Bifurcation Behavior Analysis in a Predator-Prey Model

Author

Listed:
  • Nan Wang
  • Min Zhao
  • Hengguo Yu
  • Chuanjun Dai
  • Beibei Wang
  • Pengfei Wang

Abstract

A predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and stability of the equilibria, as well as the occurrence of bifurcation behaviors (transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation), which can deduce a standard parameter controlled relationship and in turn provide a theoretical basis for the numerical simulation. Numerical analysis ensures reliability of the theoretical results and illustrates that three stable equilibria will arise simultaneously in the model. It testifies the existence of Bogdanov-Takens bifurcation, too. It should also be stressed that the dynamic evolutionary mechanism of steady conversion and bifurcation behavior mainly depend on a specific key parameter. In a word, all these results are expected to be of use in the study of the dynamic complexity of ecosystems.

Suggested Citation

  • Nan Wang & Min Zhao & Hengguo Yu & Chuanjun Dai & Beibei Wang & Pengfei Wang, 2016. "Bifurcation Behavior Analysis in a Predator-Prey Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-11, March.
    • Handle: RePEc:hin:jnddns:3565316
    DOI: 10.1155/2016/3565316
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    Cited by:

    1. Li, Xinxin & Yu, Hengguo & Dai, Chuanjun & Ma, Zengling & Wang, Qi & Zhao, Min, 2021. "Bifurcation analysis of a new aquatic ecological model with aggregation effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 75-96.

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