@techreport{817fbdb81fe24e3d8bbb268882931716,
title = "Dynamics of symmetric dynamical systems with delayed switching",
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 Poincare map near the colliding periodic orbit. The Poincar 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.",
keywords = "hysteresis, relay, invariant torus collision, delay",
author = "J Sieber and PS Kowalczyk and SJ Hogan and {di Bernardo}, M",
note = "Sponsorship: The research of J.S. and P.K. was partially supported by by EPSRC grant GR/R72020/01. ",
year = "2007",
month = dec,
day = "12",
language = "English",
type = "WorkingPaper",
}