Persistence and Critical Domain Size for Diffusing Populations with Two Sexes and Short Reproductive Season

Wen Jin, Hal Smith, Horst Thieme

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

A model is considered for a spatially distributed population of male and female individuals that mate and reproduce only once in their life during a very short reproductive season. Between birth and mating, females and males move by diffusion on a bounded domain Ω under Dirichlet boundary conditions. Mating and reproduction are described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number R0that acts as a threshold between extinction and persistence. If R0< 1 , the population dies out while it persists (uniformly weakly) if R0> 1. R0is the cone spectral radius of a bounded homogeneous map.

Original languageEnglish (US)
Pages (from-to)689-705
Number of pages17
JournalJournal of Dynamics and Differential Equations
Volume28
Issue number3-4
DOIs
StatePublished - Sep 1 2016

Keywords

  • Cone spectral radius
  • Discrete dynamical system
  • Extinction
  • Homogeneous map
  • Order permanence
  • Two-sex population

ASJC Scopus subject areas

  • Analysis

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