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

Maria A. Onyido, Rachidi B. Salako, Markjoe O. Uba and Cyril I. Udeani ()
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Maria A. Onyido: Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA
Rachidi B. Salako: Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154, USA
Markjoe O. Uba: Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA
Cyril I. Udeani: Department of Applied Mathematics and Statistics, Comenius University in Bratislava, Mlynská dolina, 84248 Bratislava, Slovakia

Mathematics, 2023, vol. 11, issue 4, 1-27

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, λ p , of the linearized system at the trivial solution: the species goes extinct if λ p ≤ 0 , while it persists uniformly in space if λ p > 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.

Keywords: nonlocal-dispersal; stage-structured model; persistence; steady state; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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