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 |
| DOIs | |
| Publication status | Published - 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 journal › Article
}
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 -