Research Of Dynamical Behaviors Of A Class Of Nonlocal System

Aiming at the non-local diffusion phenomena in nature,taking a predator-prey model with non-local diffusion as the object of study,the existence of local steady-state bifurcations of the system bifurcated by semi-trivial non-negative steady-state solutions is proved by using the eigenvalue theory of non-local operators and the classical local steady-state bifurcation theorem in infinite-dimensional dynamic systems.The specific work is as follows:Firstly,the eigenvalue problem of this kind of non-local operator is studied.The existence and uniqueness of the positive solutions of a class of non-local system are studied.A priori estimate of the positive and steady solutions for the non-local diffusion predator-prey model systems is studied.Then,by using the local steady-state bifurcation theorem and taking different system parameters as bifurcation parameters,the existence of local steady-state bifurcation from semi-trivial non-negative steady-state solution is proved.The above research results will help people to understand the dynamic behavior of this kind of non-local problem more clearly,and thus provide theoretical basis for maintaining the sustainability of the population.