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

Lili Meng, Yutao Han, Zhiyi Lu and Guang Zhang

Discrete Dynamics in Nature and Society, 2019, vol. 2019, 1-9

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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:9592878

DOI: 10.1155/2019/9592878

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