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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, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:3565316
    DOI: 10.1155/2016/3565316
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    References listed on IDEAS

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    1. Xinhong Pan & Min Zhao & Yapei Wang & Hengguo Yu & Zengling Ma & Qi Wang, 2014. "Stability and Dynamical Analysis of a Biological System," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, July.
    2. Weiwei Zhang & Min Zhao, 2013. "Dynamical Complexity of a Spatial Phytoplankton‐Zooplankton Model with an Alternative Prey and Refuge Effect," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Xinhong Pan & Min Zhao & Yapei Wang & Hengguo Yu & Zengling Ma & Qi Wang, 2014. "Stability and Dynamical Analysis of a Biological System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Weiwei Zhang & Min Zhao, 2013. "Dynamical Complexity of a Spatial Phytoplankton-Zooplankton Model with an Alternative Prey and Refuge Effect," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, May.
    5. Das, Kalyan & Gazi, Nurul Huda, 2011. "Random excitations in modelling of algal blooms in estuarine systems," Ecological Modelling, Elsevier, vol. 222(14), pages 2495-2501.
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