Spatial pattern formation driven by the cross-diffusion in a predator–prey model with Holling type functional response

Fatao Wang and Ruizhi Yang

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

Abstract: In this paper, we consider a cross-diffusion predator–prey system with Holling type functional response. We study the local stability, Turing instability, spatial pattern formation, Hopf and Turing–Hopf bifurcation of the equilibrium. Numerical simulation with zero-flux boundary conditions discloses that the system under consideration experiences the occurrence of cross-diffusion-driven instability. The dynamical system in Turing space emerges spots, stripe-spot mixtures and labyrinthine patterns, which reveals that the interaction of both self- and cross-diffusions play a significant role on the pattern formation of the present system in a way to enrich the pattern. We obtain the normal form of the Turing–Hopf bifurcation and observe that the system has stably spatially homogeneous periodic solutions, stable constant and nonconstant steady-state solutions, which indicates that the intrinsic growth rate coefficient and the environmental carrying capacity coefficient are two important factors for predator–prey system, and affect the stability of predator–prey system.

Keywords: Predator–prey; Turing instability; Hopf bifurcation; Turing–Hopf bifurcation (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007919

DOI: 10.1016/j.chaos.2023.113890

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