Gong Chen

In this paper, we put forward a time-delay ecological competition system with food restriction and diffusion terms under Neumann boundary conditions. For the case without delay, the conditions for local asymptotic stability and Turing instability are constructed. For the case with delay, the existence of Hopf bifurcation is demonstrated by analyzing the root distribution of the corresponding characteristic equations. Furthermore, by using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulas are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, some simulation examples are provided to substantiate our analysis.