Abstract
This review describes reaction-advection-diffusion models for the ecological effects and evolution of dispersal, and mathematical methods for analyzing those models. The topics covered include models for a single species, models for ecological interactions between species, and models for the evolution of dispersal strategies. The models are all set on bounded domains. The mathematical methods include spectral theory, specifically the theory of principal eigenvalues for elliptic operators, maximum principles and comparison theorems, bifurcation theory, and persistence theory.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1701-1745 |
| Number of pages | 45 |
| Journal | Discrete and Continuous Dynamical Systems- Series A |
| Volume | 34 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 2014 |
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Keywords
- Bifurcation
- Dispersal
- Ecology
- Evolution
- Persistence theory
- Population dynamics
- Reaction-diffusion
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Analysis
Cite this
Reaction-diffusion-advection models for the effects and evolution of dispersal. / Cosner, George.
In: Discrete and Continuous Dynamical Systems- Series A, Vol. 34, No. 5, 05.2014, p. 1701-1745.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Reaction-diffusion-advection models for the effects and evolution of dispersal
AU - Cosner, George
PY - 2014/5
Y1 - 2014/5
N2 - This review describes reaction-advection-diffusion models for the ecological effects and evolution of dispersal, and mathematical methods for analyzing those models. The topics covered include models for a single species, models for ecological interactions between species, and models for the evolution of dispersal strategies. The models are all set on bounded domains. The mathematical methods include spectral theory, specifically the theory of principal eigenvalues for elliptic operators, maximum principles and comparison theorems, bifurcation theory, and persistence theory.
AB - This review describes reaction-advection-diffusion models for the ecological effects and evolution of dispersal, and mathematical methods for analyzing those models. The topics covered include models for a single species, models for ecological interactions between species, and models for the evolution of dispersal strategies. The models are all set on bounded domains. The mathematical methods include spectral theory, specifically the theory of principal eigenvalues for elliptic operators, maximum principles and comparison theorems, bifurcation theory, and persistence theory.
KW - Bifurcation
KW - Dispersal
KW - Ecology
KW - Evolution
KW - Persistence theory
KW - Population dynamics
KW - Reaction-diffusion
UR - http://www.scopus.com/inward/record.url?scp=84886448910&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84886448910&partnerID=8YFLogxK
U2 - 10.3934/dcds.2014.34.1701
DO - 10.3934/dcds.2014.34.1701
M3 - Article
AN - SCOPUS:84886448910
VL - 34
SP - 1701
EP - 1745
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
SN - 1078-0947
IS - 5
ER -