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Logistic-like and Gauss coupled maps: The born of period-adding cascades

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  • da Costa, Diogo Ricardo
  • Rocha, Julia G.S.
  • de Paiva, Luam S.
  • Medrano-T, Rene O.

Abstract

In this paper we study a logistic-like and Gauss coupled maps to investigate the period-adding phenomenon, where infinite sets of periodicity (p) form a sequence in planar parameter spaces, such that, the periodicity of adjacent elements differ by a same constant (ρ) in the whole sequence (pi+1−pi=ρ). We describe the complete mechanism that form this sequence from a closed domain of isoperiodicity. Changing a control parameter, infinite different periodicities ring-shaped take place in this domain promoting regions of chaoticity. In this environment several complex sets of periodicity arise aligning themselves in sequences of period-adding, which is a common scenario that appears in a great variety of nonlinear dynamical systems. The complete process is unraveled by applying the theory of extreme orbits.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000412
    DOI: 10.1016/j.chaos.2021.110688
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    References listed on IDEAS

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    1. de Oliveira, Juliano A. & de Mendonça, Hans M.J. & da Costa, Diogo R. & Leonel, Edson D., 2018. "Effects of a parametric perturbation in the Hassell mapping," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 238-243.
    2. Varga, Roxána & Klapcsik, Kálmán & Hegedűs, Ferenc, 2020. "Route to shrimps: Dissipation driven formation of shrimp-shaped domains," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
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    4. 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.
    5. Nathan S. Nicolau & Tulio M. Oliveira & Anderson Hoff & Holokx A. Albuquerque & Cesar Manchein, 2019. "Tracking multistability in the parameter space of a Chua’s circuit model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(5), pages 1-8, May.
    6. 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.
    7. da Silva, Rafael M. & Manchein, Cesar & Beims, Marcus W., 2018. "Optimizing thermally affected ratchet currents using periodic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 454-460.
    8. 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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