On the Implementation of the 0–1 Test for Chaos

On the Implementation of the 0–1 Test for Chaos

In this paper we address practical aspects of the implementation of the 0-1 test for chaos in deterministic systems. In addition, we present a new formulation of the test which significantly increases its sensitivity. The test can be viewed as a method for distilling a binary quantity from the power...

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Veröffentlicht in:SIAM journal on applied dynamical systems 2009-01, Vol.8 (1), p.129-145
Hauptverfasser: Gottwald, Georg A., Melbourne, Ian
Format: Artikel
Sprache:eng
Schlagworte:
Applied mathematics
Chaos theory
Distillation
Dynamical systems
Dynamics
Formulations
Scholarships & fellowships
Statistical methods
Time series
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Beschreibung
Zusammenfassung:In this paper we address practical aspects of the implementation of the 0-1 test for chaos in deterministic systems. In addition, we present a new formulation of the test which significantly increases its sensitivity. The test can be viewed as a method for distilling a binary quantity from the power spectrum. The implementation is guided by recent results from the theoretical justification of the test as well as by exploring better statistical methods for determining the binary quantities. We give several examples to illustrate the improvement.
ISSN:1536-0040
1536-0040
DOI:10.1137/080718851