Spatially nonhomogeneous equilibrium in a reaction-diffusion system with distributed delay (Q631879)

The authors consider a reaction diffusion system modelling population dynamics with distributed delay, leading to a nonlinear system of integro-differential equations. First they establish the existence of positive, spatially nonhomogeneous steady state solutions and investigate the stability of these solutions. At a certain value of the minimal time delay the system undergoes a Hopf bifurcation. At the Hopf bifurcation point the authors determine the cubic term in the bifurcation equation and conclude, that the bifurcation is supercritical. Unfortunately the explanations of the applied steps are very short, so it is unclear, how the authors calculate the infinitely many center manifold coefficients, which are needed, to correctly deal with the quadratic terms in the bifurcation equations.