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Bifurcation of steady-state solutions in predator-prey and competition systems

Published online by Cambridge University Press:  14 November 2011

J. Blat  and
K. J. Brown
J. Blat
Affiliation:
Department of Mathematics, Heriot–Watt University, Riccarton, Currie, Edinburgh EH14 4AS
K. J. Brown
Affiliation:
Department of Mathematics, Heriot–Watt University, Riccarton, Currie, Edinburgh EH14 4AS
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Synopsis

We discuss steady-state solutions of systems of semilinear reaction-diffusion equations which model situations in which two interacting species u and v inhabit the same bounded region. It is easy to find solutions to the systems such that either u or v is identically zero; such solutions correspond to the case where one of the species is extinct. By using decoupling and global bifurcation theory techniques, we prove the existence of solutions which are positive in both u and v corresponding to the case where the populations can co-exist.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 21 - 34
Copyright
Copyright © Royal Society of Edinburgh 1984

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