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

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7 Citations (Scopus)

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 (Formula presented.) under Dirichlet boundary conditions. Mating and reproduction are described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number (Formula presented.) that acts as a threshold between extinction and persistence. If (Formula presented.), the population dies out while it persists (uniformly weakly) if (Formula presented.). (Formula presented.) is the cone spectral radius of a bounded homogeneous map.

Original languageEnglish (US)
JournalJournal of Dynamics and Differential Equations
DOIs
StateAccepted/In press - Feb 12 2015

Fingerprint

Persistence
Homogeneous Function
Basic Reproduction number
Spectral Radius
Extinction
Dirichlet Boundary Conditions
Bounded Domain
Cone
Die
Model

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

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title = "Persistence and Critical Domain Size for Diffusing Populations with Two Sexes and Short Reproductive Season",
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 (Formula presented.) under Dirichlet boundary conditions. Mating and reproduction are described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number (Formula presented.) that acts as a threshold between extinction and persistence. If (Formula presented.), the population dies out while it persists (uniformly weakly) if (Formula presented.). (Formula presented.) is the cone spectral radius of a bounded homogeneous map.",
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AU - Smith, Hal

AU - Thieme, Horst

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AB - 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 (Formula presented.) under Dirichlet boundary conditions. Mating and reproduction are described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number (Formula presented.) that acts as a threshold between extinction and persistence. If (Formula presented.), the population dies out while it persists (uniformly weakly) if (Formula presented.). (Formula presented.) is the cone spectral radius of a bounded homogeneous map.

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KW - Discrete dynamical system

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KW - Homogeneous map

KW - Order permanence

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