Hopf Bifurcation in a Delayed Equation with Diffusion Driven by Carrying Capacity

In this paper, a delayed reaction-diffusion equation with carrying capacity-driven diffusion is investigated. The stability of the positive equilibrium solutions and the existence of the Hopf bifurcation of the equation are considered by studying the principal eigenvalue of an associated elliptic operator. The properties of the bifurcating periodic solutions are also obtained by using the normal form theory and the center manifold reduction. Furthermore, some representative numerical simulations are provided to illustrate the main theoretical results.