Research Of Dynamics Of A Reaction-Diffusive Predator-prey System With Age-structure

In this paper,the existence and stability of solutions for a reaction-diffusion predator-prey system are studied by using qualitative and stability analysis and bifurcation theory for infinite-dimensional dynamical systems.Specific research contents are as follows:Firstly,the model with only age structure or spatial diffusion is analyzed,and the existence and stability of constant steady-state solution are proved by linearization theory.Secondly,the existence and stability of the constant steady-state solution of the reaction-diffusion predator-prey model with age structure are proved by using the linearization theory.Then,the existence of positive solutions of the model is transformed into the existence of zeros of a function by using space theory.On this basis,we give a local steady state bifurcation result of the model by using Fredholm operator theory and Crandall-Rabinowitz local bifurcation theory.Finally,by using the unilateral global bifurcation theory,we extend the local bifurcation to the whole definition space,and prove the existence of the global bifurcation of the model.The theoretical results obtained provide a theoretical reference for further understanding the dynamic behavior of this kind of model.