Dynamical collapse of trajectories

J. J. Benjamin Biemond, Alessandro P. S. de Moura, Celso Grebogi, Nathan van de Wouw, Henk Nijmeijer

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Friction induces unexpected dynamical behaviour. In the paradigmatic pendulum and double-well systems with friction, modelled with differential inclusions, distinct trajectories can collapse onto a single point. Transversal homoclinic orbits display collapse and generate chaotic saddles with forward dynamics that is qualitatively different from the backward dynamics. The space of initial conditions converging to the chaotic saddle is fractal, but the set of points diverging from it is not: friction destroys the complexity of the forward dynamics by generating a unique horseshoe-like topology. Copyright (C) EPLA, 2012

Original languageEnglish
Article number20001
Number of pages5
JournalEurophysics Letters
Issue number2
Early online date12 Apr 2012
Publication statusPublished - Apr 2012

Bibliographical note

This research was conducted during a visit of BB to the
University of Aberdeen. We would like to acknowledge
the Netherlands Organisation for Scientific Research
(NWO), the EU Network of Excellence HYCON2
(grant number 257462), and the Biotechnology and
Biological Sciences Research Council in the UK (grant
numbers BB/G001596/1 and BB-G010722) for financial


  • stick-slip
  • dry-friction
  • stability
  • systems


Dive into the research topics of 'Dynamical collapse of trajectories'. Together they form a unique fingerprint.

Cite this