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 journalArticle

1 Citation (Scopus)

Abstract

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
Volume98
Issue number2
DOIs
Publication statusPublished - Apr 2012

Keywords

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

Cite this

Dynamical collapse of trajectories. / Biemond, J. J. Benjamin; de Moura, Alessandro P. S.; Grebogi, Celso; van de Wouw, Nathan; Nijmeijer, Henk.

In: Europhysics Letters, Vol. 98, No. 2, 20001, 04.2012.

Research output: Contribution to journalArticle

Biemond, J. J. Benjamin ; de Moura, Alessandro P. S. ; Grebogi, Celso ; van de Wouw, Nathan ; Nijmeijer, Henk. / Dynamical collapse of trajectories. In: Europhysics Letters. 2012 ; Vol. 98, No. 2.
@article{484d116978684b82bb8627afe7084133,
title = "Dynamical collapse of trajectories",
abstract = "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",
keywords = "stick-slip, dry-friction, stability, systems",
author = "Biemond, {J. J. Benjamin} and {de Moura}, {Alessandro P. S.} and Celso Grebogi and {van de Wouw}, Nathan and Henk Nijmeijer",
year = "2012",
month = "4",
doi = "10.1209/0295-5075/98/20001",
language = "English",
volume = "98",
journal = "Europhysics Letters",
issn = "0295-5075",
publisher = "EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY",
number = "2",

}

TY - JOUR

T1 - Dynamical collapse of trajectories

AU - Biemond, J. J. Benjamin

AU - de Moura, Alessandro P. S.

AU - Grebogi, Celso

AU - van de Wouw, Nathan

AU - Nijmeijer, Henk

PY - 2012/4

Y1 - 2012/4

N2 - 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

AB - 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

KW - stick-slip

KW - dry-friction

KW - stability

KW - systems

U2 - 10.1209/0295-5075/98/20001

DO - 10.1209/0295-5075/98/20001

M3 - Article

VL - 98

JO - Europhysics Letters

JF - Europhysics Letters

SN - 0295-5075

IS - 2

M1 - 20001

ER -