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Organization of periodic structures in a damped-forced oscillator

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  • Fabiola Prants
  • Paulo Rech

Abstract

We report on the dynamics in a parameter plane of a continuous-time damped system driven by a periodic forcing. The dynamics is characterized by considering the Lyapunov exponents spectrum and conventional bifurcation diagrams, to discriminate periodic, quasiperiodic, and chaotic behaviors for each point in this parameter plane, according two parameters are simultaneously varied. Periodic structures born in a quasiperiodic region and embedded in a chaotic region, the so-called Arnold tongues, are observed. We show that the Arnold tongues periodic distribution is highly organized in a mixed set of two period-adding sequences. Other three typical periodic structures born and embedded in a chaotic region were observed, also individually organized in a mixed set of two period-adding sequences. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Fabiola Prants & Paulo Rech, 2014. "Organization of periodic structures in a damped-forced oscillator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(9), pages 1-4, September.
    • Handle: RePEc:spr:eurphb:v:87:y:2014:i:9:p:1-4:10.1140/epjb/e2014-50368-9
    DOI: 10.1140/epjb/e2014-50368-9
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    Citations

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    Cited by:

    1. Prants, Fabiola G. & Rech, Paulo C., 2017. "Complex dynamics of a three-dimensional continuous-time autonomous system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 132-139.
    2. da Silva, Angela & Rech, Paulo C., 2018. "Numerical investigation concerning the dynamics in parameter planes of the Ehrhard–Müller system," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 152-157.
    3. da Silva, Rodrigo A. & Rech, Paulo C., 2015. "Spiral periodic structures in a parameter plane of an ecological model," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 9-13.
    4. Wiggers, Vinícius & Rech, Paulo C., 2017. "Multistability and organization of periodicity in a Van der Pol–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 632-637.
    5. Borghezan, Monik & Rech, Paulo C., 2017. "Chaos and periodicity in Vallis model for El Niño," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 15-18.

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    Keywords

    Statistical and Nonlinear Physics;

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