https://doi.org/10.1140/epjb/s10051-022-00432-8
Regular Article - Statistical and Nonlinear Physics
Periodicity suppression and period-adding caused by a parametric excitation in the Lorenz system
Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710, Joinville, Brazil
Received:
22
April
2022
Accepted:
4
October
2022
Published online:
15
October
2022
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 
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.
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