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

Paulo C. Rech ()
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Paulo C. Rech: Universidade do Estado de Santa Catarina

The European Physical Journal B: Condensed Matter and Complex Systems, 2022, vol. 95, issue 10, 1-5

Abstract: 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

Date: 2022
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DOI: 10.1140/epjb/s10051-022-00432-8

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