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 language | English (US) |
|---|---|
| Title of host publication | Lecture Notes in Mathematics |
| Pages | 77-115 |
| Number of pages | 39 |
| Volume | 1922 |
| DOIs | |
| State | Published - 2008 |
Publication series
| Name | Lecture Notes in Mathematics |
|---|---|
| Volume | 1922 |
| ISSN (Print) | 00758434 |
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ASJC Scopus subject areas
- Mathematics (miscellaneous)
Cite this
Reaction-diffusion equations and ecological modeling. / Cosner, George.
Lecture Notes in Mathematics. Vol. 1922 2008. p. 77-115 (Lecture Notes in Mathematics; Vol. 1922).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - Reaction-diffusion equations and ecological modeling
AU - Cosner, George
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=43149108625&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=43149108625&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-74331-6_3
DO - 10.1007/978-3-540-74331-6_3
M3 - Chapter
SN - 9783540743286
VL - 1922
T3 - Lecture Notes in Mathematics
SP - 77
EP - 115
BT - Lecture Notes in Mathematics
ER -