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Periodicity suppression and period-adding caused by a parametric excitation in the Lorenz system

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  • Paulo C. Rech

    (Universidade do Estado de Santa Catarina)

Abstract

In this paper, we propose a continuous-time nonautonomous three-dimensional dynamical system, which was obtained from the original Lorenz system by introducing a parametric sinusoidal excitation. We show that, depending on the magnitude of the angular frequency of the sinusoidal excitation, two independent phenomena may occur: (i) the complete suppression of the periodic structures embedded in the chaotic region of the $$(r,\sigma )$$ ( r , σ ) parameter plane of the original Lorenz system, resulting in a chaos region completely free from periodic windows, and (ii) the appearance of other periodic structures, this time organized in period-adding sequences, embedded in the chaotic region of this same parameter plane. Graphic abstract

Suggested Citation

  • Paulo C. Rech, 2022. "Periodicity suppression and period-adding caused by a parametric excitation in the Lorenz system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(10), pages 1-5, October.
    • Handle: RePEc:spr:eurphb:v:95:y:2022:i:10:d:10.1140_epjb_s10051-022-00432-8
    DOI: 10.1140/epjb/s10051-022-00432-8
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