Dynamics Analysis Of A Leslie-Gower Predator-prey Model With Cooperative Hunting

In this paper,we mainly discuss the Leslie-Gower predator-prey ordinary d-ifferential model with cooperative hunting.We discuss the dynamics behavior of the Leslie-Gower predator-prey model with cooperative hunting.The main work includes the following two parts.In the first part,we mainly discuss the Leslie-Gower predator-prey ordinary differential model with cooperative hunting.Firstly,we analyze the influence of co-operative hunting on the existence and stability of nonnegative equilibria.Secondly,taking the hunting cooperation coefficient as a bifurcation parameter,the existence and bifurcating direction of the Hopf bifurcation of ordinary differential system are discussed.Finally we select appropriate parameters and use Matlab software for numerical simulation to verify the theoretical analysis.In the second part,firstly,for the reaction-diffusion model with prey taxis,the maximum principle,Harnack inequality and standard elliptic regularity theory are used to establish a priori estimate of non constant positive solutions.Secondly,we study the stability of nonnegative equilibrium of reaction diffusion system.Finally,taking prey-taxis coefficient as the bifurcation parameter,the local bifurcation is an-alyzed by using Crandall Rabinowitz bifurcation theory.And the global bifurcation theory is used to prove that the local bifurcation solution curve can be extended to the global bifurcation.