Stability analysis of a stage structure model with spatiotemporal delay effect

This paper is concerned with a stage structure model with spatiotemporal delay and homogeneous Dirichlet boundary condition. The existence of steady state solution bifurcating from the trivial equilibrium is obtained by using Lyapunov-Schmidt reduction. The stability analysis of the positive spatially nonhomogeneous steady state solution is investigated by a detailed analysis of the characteristic equation. Using the properties of the omega limit set, we obtain the global convergence of the solution with finite delay.