Bifurcation of relaxation oscillations in dimension two
Freddy Dumortier - Universiteit Hasselt, Campus Diepenbeek, Agoralaan - Gebouw D, B-3590 Diepenbeek, Belgium (email)
Abstract: The paper deals with the bifurcation of relaxation oscillations in two dimensional slow-fast systems. The most generic case is studied by means of geometric singular perturbation theory, using blow up at contact points. It reveals that the bifurcation goes through a continuum of transient canard oscillations, controlled by the slow divergence integral along the critical curve. The theory is applied to polynomial Liénard equations, showing that the cyclicity near a generic coallescence of two relaxation oscillations does not need to be limited to two, but can be arbitrarily high.
Keywords: Slow-fast system, bifurcation, relaxation oscillation, canard cycle, Liénard equation.
Received: December 2006; Revised: June 2007; Published: September 2007.
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