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Computational Techniques and Applications Conference and Workshops - CTAC99
September 20-24, 1999
The Australian National University
Canberra, ACT, Australia

Organizers
Mike Osborne, Bob Gingold, Steve Roberts, David Harrar II, Thanh Tran, Bob Anderssen, Henry Gardner, Markus Hegland, Lutz Grosz

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A walk through the pitchfork bifurcation
by
Rowena Ball
Dept of Theoretical Physics, RSPS&E, ANU Canberra

A walk through the pitchfork bifurcation

A walk through the pitchfork bifurcation

Discontinuous behaviour in a wide variety of dynamical systems is often ascribed to the occurrence of a pitchfork bifurcation, a codimension 2 singularity which by definition requires two additional parameters for a universal unfolding. In this work cartoons of computed bifurcation surfaces are used to visualize the pitchfork bifurcation in nonsymmetric systems and its surroundings in parameter space. It is shown that the topology of these surfaces is determined by the lower codimension antecedents of the pitchfork. In applications this means that the parameter range of jump, hysteresis, or phase transition phenomena in mathematical models (and the physical systems they purport to represent) depends on whether a transcritical or isola bifurcation factors through the pitchfork. As examples, bifurcation problems arising from several real-world dynamical models are discussed.

Date received: August 3, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadk-99.