Spatio-temporal dynamics of a reaction–diffusion–advection food-limited system with nonlocal delayed competition and Dirichlet boundary condition.

Spatio-temporal dynamics of a reaction–diffusion–advection food-limited population model with nonlocal delayed competition and Dirichlet boundary condition are considered. Existence and stability of the positive spatially nonhomogeneous steady state solution are shown. Existence and direction of the spatially nonhomogeneous steady-state-Hopf bifurcation are proved. Stable spatio-temporal patterns near the steady-state-Hopf bifurcation point are numerically obtained. We also investigate the joint influences of some important parameters including advection rate, food-limited parameter and nonlocal delayed competition on the dynamics. It is found that the effect of advection on Hopf bifurcation is opposite with the corresponding no-flux system. The theoretical results provide some interesting highlights in ecological protection in streams or rivers. [ABSTRACT FROM AUTHOR]