Coexistence Solution Analysis Of A Predator-Prey Model Of Ivlev Type With Cross Diffusion Term

Reaction diffusion system has complex and diverse properties due to its wide application background and the complexity of nonlinear terms.The existence and stability of solutions have always been an important part of the study of reactiondiffusion system.In this paper,we mainly study the predator-prey model which satisfies the Dirichlet boundary condition and whose functional response function is Ivlev type and has cross diffusion term.We use the extremum principle and comparison principle to estimate the solution of steady state system,use the topological degree theory and index theory to analyze the existence of positive solution,and use the linearization method and the eigenvalue theory to analyze the stability of the trivial solution(semi trivial solution).Finally,we use the local bifurcation theorem to analyze the bifurcation of positive solution of the system,and obtain the bifurcation of positive solution with respect to parameter.