Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model

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Abstract

An integro-differential reaction-diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase. It is claimed that this is inherently more realistic than the usual kind of reaction-diffusion model for mobile populations. Three kinds of bifurcation from the uniform steady-state solution are considered, (i) to steady spatially periodic structures, (ii) to periodic standing wave solutions, and (iii) to periodic travelling wave solutions. These correspond to aggregation and motion of populations.

LanguageEnglish
Pages1663-1688
Number of pages26
JournalSIAM Journal on Applied Mathematics
Volume50
Issue number6
DOIs
StatusPublished - Dec 1990

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Periodic Traveling Waves
Reaction-diffusion Model
Spatial Structure
Population Model
Agglomeration
Periodic structures
Aggregation
Periodic Travelling Wave Solution
Periodic Wave
Periodic Structures
Standing Wave
Steady-state Solution
Reaction-diffusion Equations
Integro-differential Equation
Bifurcation
Motion

Cite this

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title = "Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model",
abstract = "An integro-differential reaction-diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase. It is claimed that this is inherently more realistic than the usual kind of reaction-diffusion model for mobile populations. Three kinds of bifurcation from the uniform steady-state solution are considered, (i) to steady spatially periodic structures, (ii) to periodic standing wave solutions, and (iii) to periodic travelling wave solutions. These correspond to aggregation and motion of populations.",
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