Existence and stability of periodic solutions for parabolic competition systems

We consider a nonlinear reaction-diffusion competition model with Neumann boundary condition. The main goal of this article is to research the existence and uniqueness of positive periodic solution when most of parameters are functions of time t and space x. We apply the lower and upper solutions method to present existence conditions of positive periodic solution. We obtain uniqueness conditions of positive periodic solution from priori estimates of the system. Moreover, Numerical simulation is carried out to illustrate feasibility of our main results.