Spatial–temporal patterns of a two age structured population model with spatial non-locality

Abstract

The spatial–temporal patterns of the solutions to a differential equation with non-local delayed feedback that models the population dynamics of a two-stage species have been studied in this paper. The effects of the maturation time and immature mobility constant on the existence and stability of both spatially homogeneous and inhomogeneous periodic solutions are investigated by studying the Hopf bifurcation at the spatially homogeneous steady state and computing center manifold. Our results show that the bifurcated homogeneous periodic solutions are stable while inhomogeneous periodic solutions will eventually tend to homogeneous periodic solutions after transient oscillations. Furthermore, increasing of the immature mobility constant will weaken the periodic oscillation and shorten the transient oscillation time. Numerical simulations are given at last to verify our results.