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Replicate periodic windows in the parameter space of driven oscillators

Author

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  • Medeiros, E.S.
  • de Souza, S.L.T.
  • Medrano-T, R.O.
  • Caldas, I.L.

Abstract

In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation replicates these periodic windows giving rise to parameter regions correspondent to periodic orbits. The new windows are composed of parameters whose periodic orbits have the same periodicity and pattern of stable and unstable periodic orbits already existent for the unperturbed oscillator. Moreover, these unstable periodic orbits are embedded in chaotic attractors in phase space regions where the new stable orbits are identified. Thus, the observed periodic window replication is an effective oscillator control process, once chaotic orbits are replaced by regular ones.

Suggested Citation

  • Medeiros, E.S. & de Souza, S.L.T. & Medrano-T, R.O. & Caldas, I.L., 2011. "Replicate periodic windows in the parameter space of driven oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 982-989.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:11:p:982-989
    DOI: 10.1016/j.chaos.2011.08.002
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    References listed on IDEAS

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    1. de Souza, S.L.T. & Wiercigroch, M. & Caldas, I.L. & Balthazar, J.M., 2008. "Suppressing grazing chaos in impacting system by structural nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 864-869.
    2. Gallas, Jason A.C., 1994. "Dissecting shrimps: results for some one-dimensional physical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(1), pages 196-223.
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    Cited by:

    1. da Costa, Diogo Ricardo & Hansen, Matheus & Batista, Antonio Marcos, 2019. "Parametric perturbation in a model that describes the neuronal membrane potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 519-525.
    2. Trobia, José & de Souza, Silvio L.T. & dos Santos, Margarete A. & Szezech, José D. & Batista, Antonio M. & Borges, Rafael R. & Pereira, Leandro da S. & Protachevicz, Paulo R. & Caldas, Iberê L. & Iaro, 2022. "On the dynamical behaviour of a glucose-insulin model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Varga, Roxána & Klapcsik, Kálmán & Hegedűs, Ferenc, 2020. "Route to shrimps: Dissipation driven formation of shrimp-shaped domains," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. da Costa, Diogo Ricardo & Rocha, Julia G.S. & de Paiva, Luam S. & Medrano-T, Rene O., 2021. "Logistic-like and Gauss coupled maps: The born of period-adding cascades," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. de Souza, Silvio L.T. & Batista, Antonio M. & Caldas, Iberê L. & Iarosz, Kelly C. & Szezech Jr, José D., 2021. "Dynamics of epidemics: Impact of easing restrictions and control of infection spread," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. Klapcsik, Kálmán & Hegedűs, Ferenc, 2017. "The effect of high viscosity on the evolution of the bifurcation set of a periodically excited gas bubble," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 198-208.

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