Characterization of the chaos-hyperchaos transition based on return times

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
A N PavlovJ Kurths

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.

References

Jul 20, 1995·Nature·F Moss, X Pei
Aug 25, 1994·Nature·S J SchiffW L Ditto
Jun 13, 1994·Physical Review Letters·T Sauer
Jun 17, 1996·Physical Review Letters·P SoC Grebogi
Oct 14, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A N PavlovV S Anishchenko
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T KapitaniakS Popovych
Apr 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A N PavlovV S Anishchenko
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Everton G SouzaSérgio R Lopes

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