2008/01/05 by Weiming Wang, Wang, Weiming, Lei Zhang +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Evolution and Genetic Dynamics #FOS: Biological sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Populations and Evolution (q-bio.PE) #q-bio.PE
paper · pdf · doi:10.48550/arxiv.0801.0797
arxiv created 2008/01/05 · openalex publication_date 2008/01/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelis-type functional response and reaction-diffusion. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. Based on the stability and bifurcation analysis, we give the spatial pattern formation via numerical simulation, i.e., the evolution process of the model near the coexistence equilibrium point. We find that for the model we consider, pure Turing instability gives birth to the spotted pattern, pure Hopf instability gives birth to the spiral wave pattern, and both Hopf and Turing instability give birth to stripe-like pattern. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.