J Austral Math Soc Ser B 31 pp301--318, 1990.

Slowly-varying bifurcation theory in dissipative systems

J. P. Denier and R. Grimshaw

Abstract

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.

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Authors

J. P. Denier

R. Grimshaw

School of Mathematics, The University of New South Wales, Kensington, NSW, 2033, Australia.