Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge - Xiaoyuan Chang; Junjie Wei (Mathematical Biosciences and Engineering)
A diffusive predator-prey model with Holling type II functionalresponse and the no-flux boundary condition incorporating aconstant prey refuge is considered. Globally asymptoticallystability of the positive equilibrium is obtained. Regarding theconstant number of prey refuge $m$ as a bifurcation parameter, byanalyzing the distribution of the eigenvalues, the existence ofHopf bifurcation is given. Employing the center manifold theoryand normal form method, an algorithm for determining theproperties of the Hopf bifurcation is derived. Some numericalsimulations for illustrating the analysis results are carried out.