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

Bálint Kaszás, Ulrike Feudel, T. Tél

Research output: Contribution to journalArticle

4 Citations (Scopus)


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
Issue number3
Publication statusPublished - Mar 1 2018

ASJC Scopus subject areas

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

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