Dynamics Analysis Of A Predator-prey Model With Prey-Taxis And Holling-Type ?

The theory of partial differential equations is derived from the science of physic-s,chemistry,ecology,engineering and so on,with a strong practical background.The predator-prey model mainly studies the interaction between species,with im-portant significance for the protection of the ecological environment.Taking into account that the predator is always moving toward the prey,and the growth of the predator and the prey can follow the Logistic growth.In this paper,we have studied a kind of predator-prey model with prey-taxis and Holling-?.Firstly,by using the comparison principle of elliptic equations,the boundedness of any nonnegative solution is obtained.Then we give the parameter range of the unique coexistence solution.And we analyse the local stability of the constant equilibria by the linearization methods;Furthermore,the global stability of the constant equilibrium is proved by using Lyapunov function.Finally,the existence of the non-constant solution and steady state bifurcation at constant equilibrium solution is proved by using the global bifurcation theory.