### Abstract

An integro-differential reaction-diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase. It is claimed that this is inherently more realistic than the usual kind of reaction-diffusion model for mobile populations. Three kinds of bifurcation from the uniform steady-state solution are considered, (i) to steady spatially periodic structures, (ii) to periodic standing wave solutions, and (iii) to periodic travelling wave solutions. These correspond to aggregation and motion of populations.

Language | English |
---|---|

Pages | 1663-1688 |

Number of pages | 26 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 50 |

Issue number | 6 |

DOIs | |

Status | Published - Dec 1990 |

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### Cite this

**Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model.** / Britton, N. F.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model

AU - Britton, N. F.

PY - 1990/12

Y1 - 1990/12

N2 - An integro-differential reaction-diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase. It is claimed that this is inherently more realistic than the usual kind of reaction-diffusion model for mobile populations. Three kinds of bifurcation from the uniform steady-state solution are considered, (i) to steady spatially periodic structures, (ii) to periodic standing wave solutions, and (iii) to periodic travelling wave solutions. These correspond to aggregation and motion of populations.

AB - An integro-differential reaction-diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase. It is claimed that this is inherently more realistic than the usual kind of reaction-diffusion model for mobile populations. Three kinds of bifurcation from the uniform steady-state solution are considered, (i) to steady spatially periodic structures, (ii) to periodic standing wave solutions, and (iii) to periodic travelling wave solutions. These correspond to aggregation and motion of populations.

UR - http://www.scopus.com/inward/record.url?scp=0025545718&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1137/0150099

U2 - 10.1137/0150099

DO - 10.1137/0150099

M3 - Article

VL - 50

SP - 1663

EP - 1688

JO - SIAM Journal on Applied Mathematics

T2 - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 6

ER -