A Predator Prey Model With Modified Holling Type ? Response Functional

The study of the interaction between populations is of great importance to the conservation of ecology.One of the typical two species ecological models is the predator-prey model.The earliest model of predator prey model began in the United States and Italy mathematician chemist Lotka Volterra.in order to further consider the mutual interference between predators,between the two ecological population function response function from Holling type to Crowley-Martin type.Because of the development of the prey predator will always move from high density to low density of the local place,so in predator-prey system added diffusion factors will make the model more reasonable.Based on the above factors,this paper studies the reaction diffusion equations of a predator-prey model with modified Holling II response function under Neumann boundary conditions.Firstly,by comparing the principle of parabolic equations proved that the parabolic system is the existence of solutions and the boundedness.Then the linearization method and the instability of the local stability of constant solutions is analyzed by applying the principle of extremum,elliptic equations,the comparison principle gives a priori estimate of solutions of steady-state system,combined with the implicit function theorem is obtained when the diffusion coefficient is large very positive steady-state solutions of non existence.Finally,by using the theory of topological degree proved very positive steady-state solution.