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

Wen Jin; Hal Smith; Horst Thieme

doi:10.1007/s10884-015-9434-1

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 journal › Article › peer-review

15 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 language	English (US)
Pages (from-to)	689-705
Number of pages	17
Journal	Journal of Dynamics and Differential Equations
Volume	28
Issue number	3-4
DOIs	https://doi.org/10.1007/s10884-015-9434-1
State	Published - Sep 1 2016

Keywords

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

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/s10884-015-9434-1

Cite this

@article{db58d10539df4b9280dc29e353d4e191,

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 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.",

keywords = "Cone spectral radius, Discrete dynamical system, Extinction, Homogeneous map, Order permanence, Two-sex population",

author = "Wen Jin and Hal Smith and Horst Thieme",

note = "Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media New York.",

year = "2016",

month = sep,

day = "1",

doi = "10.1007/s10884-015-9434-1",

language = "English (US)",

volume = "28",

pages = "689--705",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer New York",

number = "3-4",

}

TY - JOUR

T1 - Persistence and Critical Domain Size for Diffusing Populations with Two Sexes and Short Reproductive Season

AU - Jin, Wen

AU - Smith, Hal

AU - Thieme, Horst

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

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 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.

KW - Cone spectral radius

KW - Discrete dynamical system

KW - Extinction

KW - Homogeneous map

KW - Order permanence

KW - Two-sex population

UR - http://www.scopus.com/inward/record.url?scp=84922689265&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922689265&partnerID=8YFLogxK

U2 - 10.1007/s10884-015-9434-1

DO - 10.1007/s10884-015-9434-1

M3 - Article

AN - SCOPUS:84922689265

SN - 1040-7294

VL - 28

SP - 689

EP - 705

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 3-4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this