### 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) |
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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 |
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Volume | 1922 |

ISSN (Print) | 00758434 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

*Lecture Notes in Mathematics*(Vol. 1922, pp. 77-115). (Lecture Notes in Mathematics; Vol. 1922). https://doi.org/10.1007/978-3-540-74331-6_3

**Reaction-diffusion equations and ecological modeling.** / Cosner, George.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Lecture Notes in Mathematics.*vol. 1922, Lecture Notes in Mathematics, vol. 1922, pp. 77-115. https://doi.org/10.1007/978-3-540-74331-6_3

}

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

AN - SCOPUS:43149108625

SN - 9783540743286

VL - 1922

T3 - Lecture Notes in Mathematics

SP - 77

EP - 115

BT - Lecture Notes in Mathematics

ER -