In this paper,we consider a Leslie-Gower type reaction-diffusion predator-prey system with an increasing functional response.We mainly study the effect of three different types of diffusion on the stability of this sy...In this paper,we consider a Leslie-Gower type reaction-diffusion predator-prey system with an increasing functional response.We mainly study the effect of three different types of diffusion on the stability of this system.The main results are as follows:(1)in the absence of prey diffusion,diffusion-driven instability can occur;(2)in the absence of predator diffusion,diffusion-driven instability does not occur and the non-constant stationary solution exists and is unstable;(3)in the presence of both prey diffusion and predator diffusion,the system can occur diffusion-driven instability and Turing patterns.At the same time,we also get the existence conditions of the Hopf bifurcation and the Turing-Hopf bifurcation,along with the normal form for the Turing-Hopf bifurcation.In addition,we conduct numerical simulations for all three cases to support the results of our theoretical analysis.展开更多
文摘In this paper,we consider a Leslie-Gower type reaction-diffusion predator-prey system with an increasing functional response.We mainly study the effect of three different types of diffusion on the stability of this system.The main results are as follows:(1)in the absence of prey diffusion,diffusion-driven instability can occur;(2)in the absence of predator diffusion,diffusion-driven instability does not occur and the non-constant stationary solution exists and is unstable;(3)in the presence of both prey diffusion and predator diffusion,the system can occur diffusion-driven instability and Turing patterns.At the same time,we also get the existence conditions of the Hopf bifurcation and the Turing-Hopf bifurcation,along with the normal form for the Turing-Hopf bifurcation.In addition,we conduct numerical simulations for all three cases to support the results of our theoretical analysis.
