Steady-state Analysis Of A Predator-prey Model With Generalized Holling-? Function

In nature,the interaction between species makes the population survival,and evolution.And at the same time,in order to achieve the sustainable development of ecology,resources and economy,from the beginning of the last century,the dynamics mathematical model with the interaction between various species and population environment has been carried out extensive research by ecology filed and mathematics domain experts or scholars.The predator-prey system is one of the basic relationships.We focus on the predator-prey model relationships in this article.In this paper,different diffusion coefficients are considered,and this improved model(1-3)is mainly studied in the predator-prey system with generalized Holling III function under Neumann boundary conditions.The priori estimate of the solution of the system is obtained by using the maximum principle.And then,the nonexistence of the solution is obtained by using Poincare inequality when the diffusion coefficient is large.Finally,the existence condition of the solution is obtained by using the implicit function theory.