Dynamics Analysis Of A Diffusive Predator-prey Model With Harvesting And Prey-taxis

The predator-prey model mainly studies the interaction between predators and preys.Because of its importance in the development of renewable resources and the pursuit of the best economic benefits,many scholars have studied the predator-prey model with harvesting.In the actual ecosystem,the movement of predators and preys in the habitats is not only random,but also towards the place where the preys are concentrated,which constitutes a chemotaxis phenomenon.The paper propose a diffusive predator-prey model with nonlinear Michaelis-Menten type prey harvesting and prey-taxis,linear predator harvesting subject to the homogeneous Neumann boundary condition.We show the conditions for the existence and boundedness of positive constant equilibria.We obtain the local and global stability of constant equilibria by using the eigenvalue theory and constructing a Lyapunov function.Next,a priori estimates of positive steady state solutions and nonexistence of non-constant positive solutions when the diffusion coefficient is large are obtained by applying the maximum principle and Poincare inequality.Finally,numerical simulation is used to verify the accuracy of the conclusions.