Stability And Bifurcation Analysis In A Predator-Prey Model With Nonlocal Effect And Memory-Based Diffusion

A nonlocal diffusive predator-prey model with hunting cooperation and a predatorprey model with memory-based diffusion and nonlocal effect are derived from biomathematics.The study of these two kinds of models provides theoretical support for the influence of nonlocal effect and memory-based diffusion on predator-prey models in biomathematics,which is of great significance to the development of biology.In this paper,a nonlocal diffusive predator-prey model with hunting cooperation and a predator-prey with memory-based diffusion and nonlocal are studied.This contents are as follows:In chapter one,we introduce the research background,the main research work,the innovation points and the related symbols.In chapter two,the stability and bifurcation in a nonlocal diffusive predator-prey model with hunting cooperation is studied.In the finite domain,under a rather general selection of the kernel function,we first study the stability of the positive equilibrium of the model.Then,we obtain the conditions which Hopf bifurcation and Turing bifurcation occur.In the infinite domain,choosing Top-hat kernel,Gaussian kernel and Laplace kernel as kernel function,and we mainly study the influence of Top-hat kernel function and Laplace kernel function on the stability of the positive equilibrium of the model.In chapter three,we study the stability and Hopf bifurcation in a diffusive predatorprey model with memory-based diffusion and nonlocal effect.First,we study the stability of the positive equilibrium of the model without the average memory period.Then,we choose the memory-diffusion coe cient and the average memory period as parameters to study the stability of the positive equilibrium and the existence of Hopf bifurcation.And we apply the theoretical results to investigate the predator-prey model with Holling-Ⅰ type functional response.In chapter four,we summarize and prospect the research content in chapter two and chapter three.