Stability Analysis of a Reaction-Diffusion Equation with Spatiotemporal Delay and Dirichlet Boundary Condition

In this paper, we concentrate on the study of a reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition. It is shown that a positive spatially nonhomogeneous equilibrium can bifurcate from the trivial equilibrium. Moreover, the stability of the bifurcated positive equilibrium is investigated. And we prove that, for the given spatiotemporal delay, the bifurcated equilibrium is stable under some conditions, and Hopf bifurcation cannot occur.