Global stability and Hopf bifurcation of a diffusive predator–prey model with hyperbolic mortality and prey harvesting

摘要

This paper is concerned with a predator–prey model with hyperbolic mortality and preyharvesting. The parameter regions for the stability and instability of the unique positive constantsolution of ODE and PDE are derived, respectively. Especially, the global asymptotical stability ofpositive constant equilibrium of the diffusive model is obtained by iterative technique. The stabilityand direction of periodic solutions of ODE and PDE are investigated by center manifold theoremand normal form theory, respectively. Numerical simulations are carried out to depict our theoreticalanalysis.