Complicated quasiperiodic oscillations and chaos from driven piecewise-constant circuit: Chenciner bubbles do not necessarily occur via simple phase-locking

Truong, Tri Quoc; Tsubone, Tadashi; Sekikawa, Munehisa; Inaba, Nobuyuki

doi:10.1016/j.physd.2016.09.008

Cited by 7 publications

(1 citation statement)

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“…In recent years there has been considerable interest in the study of multi-frequency quasiperiodic oscillations [1][2][3][4][5][6][7][8][9][10][11][12][13]. Such phenomena are widespread in nature and technology, in almost all areas of physics (radiophysics, electronics, laser physics, astrophysics, and many others), as well as in biology, chemistry, and medicine (see the above papers as well as monographs [14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

On two-frequency quasi-periodic perturbations of systems close to two-dimensional Hamiltonian ones with a double limit cycle

Kostromina

2021

Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki

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The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit cycle. Its solution is important both for the theory of synchronization of nonlinear oscillations and for the theory of bifurcations of dynamical systems. In the case of commensurability of the natural frequency of the unperturbed system with frequencies of quasi-periodic perturbation, resonance occurs. Averaged systems are derived that make it possible to ascertain the structure of the resonance zone, that is, to describe the behavior of solutions in the neighborhood of individual resonance levels. The study of these systems allows determining possible bifurcations arising when the resonance level deviates from the level of the unperturbed system, which generates a double limit cycle in a perturbed autonomous system. The theoretical results obtained are applied in the study of a two-frequency quasi-periodic perturbed pendulum-type equation and are illustrated by numerical computations.

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