Stability analysis of a stage structure model with spatiotemporal delay effect

Abstract

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.