Leaking in history space: A way to analyze systems subjected to arbitrary driving

Bálint Kaszás, Ulrike Feudel, T. Tél

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Our aim is to unfold phase space structures underlying systems with a drift in their parameters. Such systems are non-autonomous and belong to the class of non-periodically driven systems where the traditional theory of chaos (based e.g., on periodic orbits) does not hold. We demonstrate that even such systems possess an underlying topological horseshoe-like structure at least for a finite period of time. This result is based on a specifically developed method which allows to compute the corresponding time-dependent stable and unstable foliations. These structures can be made visible by prescribing a certain type of history for an ensemble of trajectories in phase space and by analyzing the trajectories fulfilling this constraint. The process can be considered as a leaking in history space - a generalization of traditional leaking, a method that has become widespread in traditional chaotic systems, to leaks depending on time.

Original languageEnglish
Article number033612
JournalChaos
Volume28
Issue number3
DOIs
Publication statusPublished - Mar 1 2018

Fingerprint

Trajectories
histories
Chaotic systems
Arbitrary
trajectories
Chaos theory
Phase Space
Orbits
Topological Horseshoe
Trajectory
chaos
Foliation
Period of time
Chaotic System
Periodic Orbits
orbits
Chaos
Ensemble
Unstable
History

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Leaking in history space : A way to analyze systems subjected to arbitrary driving. / Kaszás, Bálint; Feudel, Ulrike; Tél, T.

In: Chaos, Vol. 28, No. 3, 033612, 01.03.2018.

Research output: Contribution to journalArticle

Kaszás, Bálint ; Feudel, Ulrike ; Tél, T. / Leaking in history space : A way to analyze systems subjected to arbitrary driving. In: Chaos. 2018 ; Vol. 28, No. 3.
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