Dynamics Analysis Of A Predator-Prey Model With Cooperative Hunting And Stage Structure

In this paper,we study the spatiotemporal dynamics of a predator-prey model with cooperative hunting and stage structure.For the ordinary differential system,firstly,we discuss the existence of the non-negative equilibrium points.Secondly,we analyze the stability of the non-negative equilibrium points by linearization analysis and Routh-Hurwitz criterion.Thirdly,taking the hunting cooperation coefficient as a bifurcation parameter,we discuss the existence of Hopf bifurcation.Finally,we discuss the direction and the stability of the bifurcating periodic solutions.For the partial differential system,we mainly discuss the existence of noncon-stant positive equilibrium solutions for steady-state system.Firstly,we use the max-imum principle,the Harnack inequality,the strong maximum principle and the Hopf boundary lemma to establish a priori estimate of the positive solutions.Secondly,we use the implicit function theorem to discuss the non-existence of nonconstant positive steady state solutions.Finally,by using the Leray-Schauder degree theory,the existence of nonconstant positive steady state solutions is discussed.