Effect Of Starvation-driven Diffusion On The Coexistence Of A Predator-prey Model With Holling-Ⅱ Functional Response

In this paper,we study the effect of starvation-driven diffusion on the coexistence of a predator-prey model with Holling-Ⅱ functional response in spatially heterogeneous environment.The main results are as follows:In the first part,the stability of the semi-trivial solution in the uniform diffusion case and the starvation-driven diffusion case are analyzed by using the eigenvalue theory,and the boundary curves of the stability of the semi-trivial solution in the two diffusion cases are drawn.The results showed that the semi-trivial solution instability area in the case of starvation-driven diffusion is larger,which means that starvation-driven diffusion is beneficial to species coexistence.In the second part,the existence and uniqueness of system coexistence solutions in the case of uniform diffusion and the case of starvation-driven diffusion are discussed respectively.Firstly,the maximum principle is used to establish the priori estimate of the positive equilibrium solution,secondly,the existence of the coexistence solution is discussed by the fixed point index theory,and finally the regularity theory of the elliptic equation is used to study the uniqueness of the coexistence solution.In the third part,the local bifurcation theory is applied to analyze the local branching structure in the case of starvation-driven diffusion.Taking the starvationdriven diffusion coefficient as the bifurcation parameter,firstly the existence of the positive solution of local bifurcation is obtained,secondly the branching direction is determined near the branching point,and finally the stability of the local branching solution is investigated.