Reaction-diffusion equations and ecological modeling

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Scopus citations

Abstract

Reaction-diffusion equations are widely used as models for spatial effects in ecology. They support three important types of ecological phenomena: the existence of a minimal patch size necessary to sustain a population, the propagation of wavefronts corresponding to biological invasions, and the formation of spatial patterns in the distributions of populations in homogeneous environments. Reaction-diffusion equations can be analyzed by means of methods from the theory of partial differential equations and dynamical systems. we will discuss the derivation of reaction-diffusion models in ecology, sketch the basic aspects of their analysis, and describe some of their applications and mathematical properties.

Original languageEnglish (US)
Title of host publicationTutorials in Mathematical Biosciences IV
Subtitle of host publicationEvolution and Ecology
PublisherSpringer Verlag
Pages77-115
Number of pages39
ISBN (Print)9783540743286
DOIs
StatePublished - Jan 1 2008

Publication series

NameLecture Notes in Mathematics
Volume1922
ISSN (Print)0075-8434

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ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Cosner, C. (2008). Reaction-diffusion equations and ecological modeling. In Tutorials in Mathematical Biosciences IV: Evolution and Ecology (pp. 77-115). (Lecture Notes in Mathematics; Vol. 1922). Springer Verlag. https://doi.org/10.1007/978-3-540-74331-6_3