Hopf Bifurcation of Delayed Predator-Prey System with Reserve Area for Prey and in the Presence of Toxicity (Communications in Mathematical Research, 2019)
A kind of three species delayed predator-prey system with reserve areafor prey and in the presence of toxicity is proposed in this paper. Local stability ofthe coexistence equilibrium of the system and the existence of a Hopf bifurcation isestablished by choosing the time delay as the bifurcation parameter. Explicit formulas to determine the direction and stability of the Hopf bifurcation are obtained bymeans of the normal form theory and the center manifold theorem. Finally, we givea numerical example to illustrate the obtained results.