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On the characterization of the basin of attraction of limit cycles
by
Peter Giesl
TU München
Although limit cycles are - besides equilibria - the simplest attractors in dynamical systems there is no straight-forward way to prove their existence and uniqueness, in general. The determination of their basin of attraction is an even more difficult task. We consider a smooth dynamical system given by an autonomous ordinary differential equation. We give a sufficient local condition for a subset of the phase space Rn to belong to the basin of attraction of a unique limit cycle without assuming its existence. Instead, existence and uniqueness are conclusions. It turns out that this condition becomes sufficient and necessary, if we equip the phase space with an appropriate Riemannian metric. Thus, we can characterize the basin of attraction of a limit cycle. Also, based on the idea of this proof we present an algorithm to prove existence of a limit cycle and to determine a part of its basin of attraction.
http://www-m8.mathematik.tu-muenchen.de/personen/giesl/
Date received: March 27, 2001
Copyright © 2001 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 # cafv-88.