The Effects Of Diffusion And Spatial Heterogeneity In The Leslie-Gower Predator-prey Model

In the development of biomathematics,the study of dynamic analysis of biological population models has become an important research direction.With the deepening of the research,scholars found the diffusion phenomenon is widespread in the interaction between biological populations.In addition,the influence of spatial environment on biological population can not be ignored.Therefor,Many scholars have introduced diffusion and spatial heterogeneity into the model,and studied the influence of these two factors on species dynamics behavior.Diffusive predator-prey model is very important in the practical application of biological population dynamics behavior.Based on the specific biological model as the theoretical background,by virtue of the comparison principle,linearization principle,combined with the related properties of linear logistic diffusion equation,the generalized response function Leslie-Gower predator-prey model is studied in this paper.In this paper,we mainly study a diffusive Leslie-Gower predator-prey model in spatial heterogeneous environment,further optimize the response function,and obtain the related properties of the solution,such as the global existence.Then,we use the linear logistic diffusion equation to analyze the principal eigenvalues.The local stability of the semi trivial steady state solution under different conditions is obtained,and the results are verified by numerical simulation.On this basis,the global stability of the semi trivial steady state solution is obtained by strengthening the conditions.After that,we estimate the solution of the system a priori and discuss the influence of the diffusion coefficient on the asymptotic behavior of the steady state solution.Finally,We take the diffusion coefficient as the bifurcation parameter,consider the local bifurcation behavior of the steady-state solution,and prove the existence and stability of the bifurcation of the steady-state solution.