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Slowly-varying bifurcation theory in dissipative systems

Published online by Cambridge University Press:  17 February 2009

J. P. Denier  and
R. Grimshaw
R. Grimshaw
Affiliation:
School of Mathematics, The University of New South Wales, Kensington, NSW, 2033, Australia.
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Abstract

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Systems of coupled nonlinear differential equations with an externally controlled slowly-varying bifurcation parameter are considered. Canonical equations governing the transition between bifurcated solutions are derived by making use of methods of “steady” bifurcation theory. It is found that, depending on the initial amplitudes, the solutions of the transition equations are either asymptotically equivalent to the bifurcated solutions or the solutions develop algebraic singularities at some positive finite time. These singularities correspond to a transition to a solution of a fully nonlinear problem.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 3 , January 1990 , pp. 301 - 318
Copyright
Copyright © Australian Mathematical Society 1990

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