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Phys. Rev. E 54, R3082–R3085 (1996)

Tool to recover scalar time-delay systems from experimental time series

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M. J. Bünner, M. Popp, Th. Meyer, A. Kittel, and J. Parisi*
Physical Institute, University of Bayreuth, D-95440 Bayreuth, Germany

Received 8 December 1995; revised 31 July 1996; published in the issue dated October 1996

We propose a method that is able to analyze chaotic time series gained from experimental data. The method allows us to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay differential equation of the form dy(t)/dt=h(y(t), y(t-τ0)), the delay time τ0 and the function h can be recovered. There are no restrictions to the dimensionality of the chaotic attractor. It turns out that the method is not strongly sensitive to additional noise. We successfully apply the method to various time series taken from a computer experiment and two different electronic oscillators.

© 1996 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.54.R3082
DOI:
10.1103/PhysRevE.54.R3082
PACS:
05.45.+b

*Author to whom correspondence should be addressed: Prof. Dr. Jürgen Parisi, Physical Institute, University of Bayreuth, D-95440 Bayreuth, Germany.

 
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