Periodic solutions of a spatiotemporal predator-prey system with additional food

In this paper, a spatiotemporal predator-prey system with additional food supplied is investigated. By analyzing eigenvalues of the characteristic equation associated with delay parameter, the conditions of the existence of Hopf bifurcation in one dimension space are obtained. We analyze the properties of bifurcating period solutions based on the normal form theory and the center manifold theorem of partial functional differential equations (PFDs). Furthermore, numerical simulations confirm the theoretical results. The obtained results may provide some new insights on periodic oscillation in the densities of predator and prey.