Hopf bifurcation analysis of a reaction–diffusion Sel'kov system

A reaction–diffusion system known as the Sel'kov model subject to the homogeneous Neumann boundary condition is investigated, where detailed Hopf bifurcation analysis is performed. We not only show the existence of the spatially homogeneous/non-homogeneous periodic solutions of the system, but also derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution.