Small-scale instabilities in dynamical systems with sliding

J. Sieber, P. Kowalczyk

Research output: Contribution to journalArticle

72 Downloads (Pure)


We demonstrate with a minimal example that in Filippov systems (dynamical systems governed by discontinuous but piecewise smooth vector fields) stable periodic motion with sliding is not robust with respect to stable singular perturbations. We consider a simple dynamical system that we assume to be a quasi-static approximation of a higher-dimensional system containing a fast stable subsystem. We tune a system parameter such that a stable periodic orbit of the simple system touches the discontinuity surface: this is the so-called grazing-sliding bifurcation. The periodic orbit remains stable, and its local return map becomes piecewise linear. However, when we take into account the fast dynamics the local return map of the periodic orbit changes qualitatively, giving rise to, for example, period-adding cascades or small-scale chaos.
Original languageEnglish
Pages (from-to)44-57
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
Publication statusPublished - Jan 2010


Dive into the research topics of 'Small-scale instabilities in dynamical systems with sliding'. Together they form a unique fingerprint.

Cite this