Dynamical collapse of trajectories

J.J.B. Biemond, A.P.S. Moura, de, C. Grebogi, N. Wouw, van de, H. Nijmeijer

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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.
Original languageEnglish
Article number20001
Pages (from-to)20001-1/6
JournalEPL
Volume98
Issue number2
DOIs
Publication statusPublished - 2012

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    Biemond, J. J. B., Moura, de, A. P. S., Grebogi, C., Wouw, van de, N., & Nijmeijer, H. (2012). Dynamical collapse of trajectories. EPL, 98(2), 20001-1/6. [20001]. https://doi.org/10.1209/0295-5075/98/20001