Direction of Hopf bifurcation in a delayed Lotka–Volterra competition diffusion system

This paper is concerned with a delayed Lotka–Volterra two species competition diffusion system with a single discrete delay and subject to homogeneous Dirichlet boundary conditions. The main purpose is to investigate the direction of Hopf bifurcation resulting from the increase of delay. By applying the implicit function theorem, it is shown that the system under consideration can undergo a supercritical Hopf bifurcation near the spatially inhomogeneous positive stationary solution when the delay crosses through a sequence of critical values.