Stability and Hopf bifurcation for a stage-structured predator-prey model incorporating refuge for prey and additional food for predator

In this paper, we study a stage-structured predator-prey model incorporating refuge for prey and additional food for predator. By analyzing the corresponding characteristic equations, we investigate the local stability of equilibria and the existence of Hopf bifurcation at the positive equilibrium taking the time delay as a bifurcation parameter. Furthermore, we obtain the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions applying the center manifold theorem and normal form theory. Numerical simulations are illustrated to verify our main results.