Abstract
A diffusive prey–predator system with Holling type III response function incorporating a prey refuge subject to Neumann boundary conditions is considered. The sufficient conditions are given to ensure that the equilibria are local and global asymptotically stable, respectively. And the existence of Hopf bifurcation at the positive equilibrium is obtained by regarding prey refuge as parameter. By the theory of normal form and center manifold, a algorithm for determining the direction and stability of Hopf bifurcation is derived. Some numerical simulations are carried out for illustrating the analytic results.
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