Multiple Bifurcation Analysis in a Diffusive Eco-Epidemiological Model with Time Delay

Abstract

In this paper, a delayed eco-epidemiological model with diffusion effects and homogeneous Neumann boundary conditions is proposed. Sufficient conditions for the occurrence of the Hopf-zero, Takens–Bogdanov and saddle-node bifurcations at several steady states are derived. By taking the delay as the bifurcation parameter, it was shown that spatially homogeneous and nonhomogeneous Hopf bifurcations occur at several steady states for a sequence of critical values of the delay parameter. In addition, by applying the normal form theory and center manifold theorem for partial functional differential equations, we present the explicit formula for determining the properties of spatial Hopf bifurcations. Some numerical simulations are carried out.