Properties and numerical simulations of positive solutions for a variable-territory model

In this paper, we consider a variable-territory predator–prey model with Dirichlet boundary condition. We establish a necessary and sufficient condition for the existence of positive solutions to steady state. Furthermore, we also prove that the local bifurcation positive solutions are unconditional stable. By regular perturbation theorem, we investigate the convergence and stability of positive solutions when handling time m is large enough. At the end of this paper, there are some numerical simulations and biological significance to check and complement our theoretical analysis results.