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Chaos / Volume 20 / Issue 4 / REGULAR ARTICLES

Chaos 20, 043115 (2010); http://dx.doi.org/10.1063/1.3498731 (11 pages)

Recurrence-based detection of the hyperchaos-chaos transition in an electronic circuit

E. J. Ngamga1, A. Buscarino2, M. Frasca2,3, G. Sciuto3, J. Kurths1,4, and L. Fortuna2,3

1Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Germany
2Laboratorio sui Sistemi Complessi, Scuola Superiore di Catania, Università degli Studi di Catania, Via S. Nullo 5/i, 95125 Catania, Italy
3Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi, Facoltà di Ingegneria, Università degli Studi di Catania, viale A. Doria 6, 95125 Catania, Italy
4Institute of Physics, Humboldt University Berlin, 12489 Berlin, Germany

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(Received 23 April 2010; accepted 17 September 2010; published online 11 November 2010)

Some complex measures based on recurrence plots give evidence about hyperchaos-chaos transitions in coupled nonlinear systems [ E. G. Souza et al., “Using recurrences to characterize the hyperchaos-chaos transition,” Phys. Rev. E 78, 066206 (2008) ]. In this paper, these measures are combined with a significance test based on twin surrogates to identify such a transition in a fourth-order Lorenz-like system, which is able to pass from a hyperchaotic to a chaotic behavior for increasing values of a single parameter. A circuit analog of the mathematical model has been designed and implemented and the robustness of the recurrence-based method on experimental data has been tested. In both the numerical and experimental cases, the combination of the recurrence measures and the significance test allows to clearly identify the hyperchaos-chaos transition.

© 2010 American Institute of Physics

Lead Paragraph

Dynamical systems show a wide range of complex behavior depending on certain order parameters. When the mathematical model of a dynamical system is known, the Lyapunov spectrum can be calculated in a quite accurate way, allowing the extraction of information needed to characterize the system’s behavior. In fact, one positive Lyapunov exponent is related to a chaotic behavior, while two or more positive exponents are a signature of hyperchaos.1 However, in many applications the mathematical model is not available, but only time series are observable. In these cases, the analysis of recurrences can give important insights for the detection of transitions in the dynamical behavior. The aim of this paper is to detect a hyperchaos-chaos transition numerically and experimentally in a fourth-order Lorenz-like system, which, by varying the value of a single parameter, can exhibit periodic, chaotic, and even hyperchaotic oscillations. Starting from recently introduced recurrence-based measures2 and using the numerical equations, the hyperchaos-chaos transition is identified and confirmed by a statistical test. Moreover, the same recurrence method is applied to a suitably designed and implemented electronic circuit able to mimic the behavior of the considered dynamical model.

Article Outline

  1. INTRODUCTION
  2. CHARACTERIZATION OF THE HYPERCHAOS-CHAOS TRANSITION
  3. NUMERICAL ANALYSIS OF THE HYPERCHAOS-CHAOS TRANSITION IN A LORENZ-LIKE HYPERCHAOTIC SYSTEM
  4. EXPERIMENTAL ANALYSIS OF THE HYPERCHAOS-CHAOS TRANSITION IN THE LORENZ-LIKE HYPERCHAOTIC CIRCUIT
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

chaos, nonlinear dynamical systems

PACS

  • 05.45.Ra

    Coupled map lattices

  • 05.45.Gg

    Control of chaos, applications of chaos

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3498731

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    E. G. Souza, R. L. Viana, and S. R. Lopes, “Using recurrences to characterize the hyperchaos-chaos transition,” Phys. Rev. E 78, 066206 (2008).

    M. Thiel, M. C. Romano, P. L. Read, and J. Kurths, “Estimation of dynamical invariants without embedding by recurrence plots,” Chaos 14, 234 (2004)CHAOEH000014000002000234000001.

    E. J. Ngamga, A. Nandi, R. Ramaswamy, M. C. Romano, M. Thiel, and J. Kurths, “Recurrence analysis of strange nonchaotic dynamics,” Phys. Rev. E 75, 036222 (2007).

    E. J. Ngamga, A. Buscarino, M. Frasca, L. Fortuna, A. Prasad, and J. Kurths, “Recurrence analysis of strange nonchaotic dynamics in driven excitable systems,” Chaos 18, 013128 (2008)CHAOEH000018000001013128000001.

    T. Kapitaniak, Y. Maistrenko, and S. Popovych, “Chaos-hyperchaos transition,” Phys. Rev. E 62, 1972 (2000).

    M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193 (1997).

    R. Hegger, H. Kantz, and T. Schreiber, “Practical implementation of nonlinear time series methods: The TISEAN package,” Chaos 9, 413 (1999)CHAOEH000009000002000413000001.


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