In this paper we give an overview of some aspects of chaotic dynamics in hybrid systems, which comprise different types of behaviour. Hybrid systems may exhibit discontinuous dependence on initial conditions leading to new dynamical phenomena. We indicate how methods from topological dynamics and ergodic theory may be used to study hybrid systems, and review existing bifurcation theory for one-dimensional non-smooth maps, including the spontaneous formation of robust chaotic attractors. We present case studies of chaotic dynamics in a switched arrival system and in a system with periodic forcing.
Additional Metadata
Keywords chaotic dynamics, hybrid systems, symbolic dynamics, nonsmooth bifurcations
MSC Differential equations with impulses (msc 34A37), Symbolic dynamics (msc 37B10), Nonsingular (and infinite-measure preserving) transformations (msc 37A40), Discontinuous equations (msc 34A36), Attractors and their bifurcations (msc 37G35)
THEME Life Sciences (theme 5), Energy (theme 4)
Publisher CWI
Series Modelling, Analysis and Simulation [MAS]
Project Computational Topology for Systems and Control
Note This research was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) Vidi grant 639.032.408
Citation
Collins, P.J. (2008). Chaotic dynamics in hybrid systems. Modelling, Analysis and Simulation [MAS]. CWI.