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Nonlinear Dynamics

, Volume 78, Issue 2, pp 1477–1487 | Cite as

Efficient detection of the quasi-periodic route to chaos in discrete maps by the three-state test

  • J. S. Armand Eyebe FoudaEmail author
  • Wolfram Koepf
Original Paper

Abstract

The three-state test (3ST) is a method based on ordinal pattern analysis for detecting chaos and determining the period in time series. For some well-known chaotic dynamical systems, we showed that the test behaves similar to Lyapunov exponents. However, the 3ST is detecting quasi-periodic motions both as regular and non-regular. In this paper, we propose to use the sensitivity of its chaos indicator \(\lambda \) on time delay for clear discernment between quasi-periodic and chaotic dynamics. Simulation results obtained using the logistic map and the sine-circle map attest that the sensitivity of \(\lambda \) on time delay is sufficient for the detection of the periodic and quasi-periodic route to chaos. A comparison with the permutation entropy confirms the effectiveness of the 3ST for the analysis of discrete time series data.

Keywords

Time series analysis Ordinal patterns Permutation entropy Chaos detection 3ST 

Notes

Acknowledgments

This work was supported by a DAAD scholarship.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Physics, Faculty of ScienceUniversity of Yaoundé IYaoundéCameroon
  2. 2.Institute of MathematicsUniversity of KasselKasselGermany

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