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Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model

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  • Lili Meng
  • Yutao Han
  • Zhiyi Lu
  • Guang Zhang

Abstract

In this paper, a discrete predator-prey system with the periodic boundary conditions will be considered. First, we get the conditions for producing Turing instability of the discrete predator-prey system according to the linear stability analysis. Then, we show that the discrete model has the flip bifurcation and Turing bifurcation under the critical parameter values. Finally, a series of numerical simulations are carried out in the Turing instability region of the discrete predator-prey model; some new Turing patterns such as striped, bar, and horizontal bar are observed.

Suggested Citation

  • Lili Meng & Yutao Han & Zhiyi Lu & Guang Zhang, 2019. "Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-9, April.
    • Handle: RePEc:hin:jnddns:9592878
    DOI: 10.1155/2019/9592878
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