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Doubly Transient Chaos: Generic Form of Chaos in Autonomous Dissipative Systems

Adilson E. Motter, Márton Gruiz, György Károlyi, and Tamás Tél
Phys. Rev. Lett. 111, 194101 – Published 7 November 2013
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Abstract

Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final state sensitivity observed in connection with fractal basin boundaries in conservative scattering systems and driven dissipative systems. Here we focus on the most prevalent case of undriven dissipative systems, whose transient dynamics fall outside the scope of previous studies since no time-dependent solutions can exist for asymptotically long times. We show that such systems can exhibit positive finite-time Lyapunov exponents and fractal-like basin boundaries which nevertheless have codimension one. In sharp contrast to its driven and conservative counterparts, the settling rate to the (fixed-point) attractors grows exponentially in time, meaning that the fraction of trajectories away from the attractors decays superexponentially. While no invariant chaotic sets exist in such cases, the irregular behavior is governed by transient interactions with transient chaotic saddles, which act as effective, time-varying chaotic sets.

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  • Received 16 August 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.194101

© 2013 American Physical Society

Synopsis

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Transiently Chaotic

Published 7 November 2013

A new form of chaotic behavior could appear in systems in which every motion dies out because of the effects of dissipation.

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Authors & Affiliations

Adilson E. Motter1, Márton Gruiz2, György Károlyi3, and Tamás Tél2,4

  • 1Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
  • 2Institute for Theoretical Physics, Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
  • 3Institute of Nuclear Techniques, Budapest University of Technology and Economics, Műegyetem rakpart 9, 1111 Budapest, Hungary
  • 4Theoretical Physics Research Group of the Hungarian Academy of Sciences at Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary

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Issue

Vol. 111, Iss. 19 — 8 November 2013

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