Dynamics of symmetric dynamical systems with delayed switching
Journal of Vibration and Control
© 2017 SAGE Publications Los Angeles, London, New Delhi, Singapore. Posted here by permission of SAGE Publications
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 Poincare map near the colliding periodic orbit. The Poincare 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.
The research of JS and PK was partially supported by EPSRC grant GR/R72020/01
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.
Vol 16(7–8): pp.1111–1140