Dynamics of symmetric dynamical systems with delayed switching

J. Sieber, P. Kowalczyk, S. J. Hogan, M. Di Bernardo

Research output: Contribution to journalArticle (Academic Journal)

13 Citations (Scopus)

Abstract

We study dynamical systems that switch between two different vector fields depending on a discrete variable and with a delay. When the delay reaches a problem-dependent critical value, so-called event collisions occur. This paper classifies and analyzes event collisions, a special type of discontinuity-induced bifurcations, for periodic orbits. Our focus is on event collisions of symmetric periodic orbits in systems with full reflection symmetry, a symmetry that is prevalent in applications. We derive an implicit expression for the Poincaré map near the colliding periodic orbit. The Poincaré map is piecewise smooth, finite-dimensional, and changes the dimension of its image at the collision. In the second part of the paper we apply this general result to the class of unstable linear single-degree-of-freedom oscillators where we detect and continue numerically collisions of invariant tori. Moreover, we observe that attracting closed invariant polygons emerge at the torus collision.
Original languageEnglish
Pages (from-to)1111-1140
Number of pages30
JournalJournal of Vibration and Control
Volume16
Issue number7-8
DOIs
Publication statusPublished - Jul 2010

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