Korobeinikov, Andrei and Norbury, John and Wake, Graeme (2007) *Long-term coexistence for a competitive system of spatially varying gradient reaction-diffusion equations.* Nonlinear Analysis Series B: Real World Applications . ISSN 1468-1218 (Submitted)

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## Abstract

Spatial distribution of interacting chemical or biological species is usually described by a system of reaction-diffusion equations. In this work we consider a system of two reaction diffusion equations with spatially varying diffusion coefficients which are different for different species and with forcing terms which are the gradient of a spatially varying potential. Such a system describes two competing biological species. We are interested in the possibility of long-term coexistence of the species in a bounded domain. Such long-term coexistence may be associated either with a periodic in time solution (usually associated with a Hopf bifurcation), or with time-independent solutions. We prove that no periodic solution exists for the system. We also consider some steady-states (the time-independent solutions) and examine their

stability and bifurcations.

Item Type: | Article |
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Subjects: | O - Z > Partial differential equations |

Research Groups: | Oxford Centre for Industrial and Applied Mathematics |

ID Code: | 638 |

Deposited By: | Richard Booth |

Deposited On: | 22 Aug 2007 |

Last Modified: | 20 Jul 2009 14:23 |

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