Stability Analysis Of Reaction-diffusion Equation With Holling ? Predation

Boreal forest in Canada has two main recurrent disturbances:one is fire and the other one is spruce budworm.The spruce budworm is extremely destructive,and its outbreak can cause huge damage.Therefore,it is of great significance to establish an appropriate mathematical model to study its dynamic behavior.This paper mainly studies the dynamic behavior of diffusion equation with Holling ?predation.The main contents are divided into the following three parts.Firstly,we study the ordinary differential equation model when the diffusion coefficient is zero.Through the description and analysis of its steady state solution,the dynamic behavior of the positive solution of ordinary differential equation is obtained.Secondly,the reaction-diffusion equation with Dirichlet boundary condition and Neumann boundary condition are studied respectively.By considering the existence of steady-state solutions under different parameter conditions,the stability of the steady-state solution is judged to further study the dynamic behavior of the positive solution.Finally,we study the corresponding nonlocal problems and analyze the dynamic behavior of positive solutions.Our results also exhibit the different effects of boundary conditions on the dynamic behavior of positive solutions.