Characterization of the chaos-hyperchaos transition based on return times

A. N. Pavlov, O. N. Pavlova, Y. K. Mohammad, Jurgen Kurths

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We discuss the problem of the detection of hyperchaotic oscillations in coupled nonlinear systems when the available information about this complex dynamical regime is very limited. We demonstrate the ability of diagnosing the chaos-hyperchaos transition from return times into a Poincaré section and show that an appropriate selection of the secant plane allows a correct estimation of two positive Lyapunov exponents (LEs) from even a single sequence of return times. We propose a generalized approach for extracting dynamics from point processes that allows avoiding spurious identification of the dynamical regime caused by artifacts. The estimated LEs are nearly close to their expected values if the second positive LE is essentially different from the largest one. If both exponents become nearly close, an underestimation of the second LE may be obtained. Nevertheless, distinctions between chaotic and hyperchaotic regimes are clearly possible.
Original languageEnglish
Article number022921
Number of pages5
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number2
Publication statusPublished - Feb 2015

Bibliographical note

This work was supported by the Russian Science Foundation (Agreement 14-12-00224)


  • hyperchaotic oscillations
  • chaos-hyperchaos transition


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