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Global higher bifurcations in coupled systems of nonlinear eigenvalue problems

Published online by Cambridge University Press:  14 November 2011

Robert Stephen Cantrell
Robert Stephen Cantrell
Affiliation:
Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124, U.S.A.
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Synopsis

Coexistent steady-state solutions to a Lotka–Volterra model for two freely-dispersing competing species have been shown by several authors to arise as global secondary bifurcation phenomena. In this paper we establish conditions for the existence of global higher dimensional n-ary bifurcation in general systems of multiparameter nonlinear eigenvalue problems which preserve the coupling structure of diffusive steady-state Lotka–Volterra models. In establishing our result, we mainly employ the recently-developed multidimensional global multiparameter theory of Alexander–Antman. Conditions for ternary steady-state bifurcation in the three species diffusive competition model are given as an application of the result.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 1-2 , 1987 , pp. 113 - 120
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

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