Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model. (1st April 2019)

• Record Type: Journal Article
• Authors: Meng, Lili; Han, Yutao; Lu, Zhiyi; Zhang, Guang
• Other Names: Anderson Douglas R. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2019(2019)
• Publication Date: 2019-04-01
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2019/9592878
• Languages: English
• ISSNs: 1026-0226

Abstract

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.