Dynamical collapse of trajectories

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

doi:10.1209/0295-5075/98/20001

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 journal › Article › peer-review

2 Citations (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 language	English
Article number	20001
Number of pages	5
Journal	Europhysics Letters
Volume	98
Issue number	2
Early online date	12 Apr 2012
DOIs	https://doi.org/10.1209/0295-5075/98/20001
Publication status	Published - Apr 2012

Keywords

stick-slip
dry-friction
stability
systems

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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",

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 support.",

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AU - Grebogi, Celso

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AU - Nijmeijer, Henk

N1 - 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 support.

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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

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KW - systems

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Dynamical collapse of trajectories

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