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

Abstract EN

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.