### 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 | Tutorials in Mathematical Biosciences IV |

Subtitle of host publication | Evolution and Ecology |

Publisher | Springer Verlag |

Pages | 77-115 |

Number of pages | 39 |

ISBN (Print) | 9783540743286 |

DOIs | |

State | Published - Jan 1 2008 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 1922 |

ISSN (Print) | 0075-8434 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*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