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 journalArticle

16 Citations (Scopus)

Abstract

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
Volume91
Issue number2
DOIs
Publication statusPublished - Feb 2015

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Hyperchaos
Return Time
Lyapunov Exponent
chaos
Chaos
exponents
Point Process
Chord or secant line
Expected Value
Coupled System
nonlinear systems
Nonlinear Systems
Exponent
Oscillation
artifacts
oscillations
Demonstrate

Keywords

  • hyperchaotic oscillations
  • chaos-hyperchaos transition

Cite this

Characterization of the chaos-hyperchaos transition based on return times. / Pavlov, A. N. ; Pavlova, O. N.; Mohammad, Y. K. ; Kurths, Jurgen.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 91, No. 2, 022921 , 02.2015.

Research output: Contribution to journalArticle

Pavlov, A. N. ; Pavlova, O. N. ; Mohammad, Y. K. ; Kurths, Jurgen. / Characterization of the chaos-hyperchaos transition based on return times. In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics. 2015 ; Vol. 91, No. 2.
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