Dynamics of Classical Solutions of a Two-Stage Structured Population Model with Nonlocal Dispersal

Abstract

We study the dynamics of classical solutions of a two-stage structured population model with nonlocal dispersal in a spatially heterogeneous environment and address the question of the persistence of the species. In particular, we show that the species’ persistence is completely determined by the sign of the principal spectrum point, λp, of the linearized system at the trivial solution: the species goes extinct if λp≤0, while it persists uniformly in space if λp>0. Sufficient conditions are provided to guarantee the existence, uniqueness, and stability of a positive steady state when the parameters are spatially heterogeneous. Furthermore, when the model parameters are spatially homogeneous, we show that the unique positive equilibrium is globally stable with respect to positive perturbations.