Spatial Patterns of a Predator-prey Model with Prey Refuge and Nonlocal Predation Effect
Predator-prey reaction-diffusion model with refuge effect is an important type of population dynamics model,and its pattern formation provides key information for studying the spatiotemporal distribution of population.A Leslie-Gower predator-prey reaction-diffusion model with both refuge and nonlocal predation effects is proposed.Firstly,the conditions for local stability and Turing instability of the positive equilibrium point are derived through linear stability analysis and Turing instability analysis,respectively.Secondly,the evolution of the patterns of the prey with nonlocal predation and refuge effects was demonstrated through numerical simulations.Finally,by analyzing the relationship between the spatial mean density of predator and prey populations and the changes in nonlocal prey and refuge effect parameters,it is shown that the spatial mean density of prey increases,while the number of predator decreases with the enhancement of nonlocal predation effects,indicating that nonlocal effects promote the growth of prey density while inhibiting the growth of predator populations;The spatial mean density of predator and prey increases simultaneously with the enhancement of refuge effect,indicating that strong refuge effect has a protective effect on prey and can promote the persistence and coexistence of predator and prey.The result helps people better understand the law of nonlocal effects and refuge effects on the pattern formation of predator and prey from a mathematical perspective.
prey refugenonlocal predation effectpatternpredator-prey modelreaction diffusion system
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