A ring generator of two- and three-frequency quasiperiodic self-oscillations based on the van der Pol oscillator

In this work, we present a model of an autonomous three-mode ring generator based on the van der Pol oscillator, where periodic, two-frequency quasiperiodic, three-frequency quasiperiodic, and chaotic self-oscillations are observed. The transitions to chaos occur as a result of a sequence of torus d...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2021-08, Vol.31 (8), p.083108-083108
Main Authors: Astakhov, Sergey V., Astakhov, Oleg V., Fadeeva, Natalia S., Astakhov, Vladimir V.
Format: Article
Language:English
Subjects:
Bifurcations
Oscillations
Synchronism
Time synchronization
Toruses
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Summary:In this work, we present a model of an autonomous three-mode ring generator based on the van der Pol oscillator, where periodic, two-frequency quasiperiodic, three-frequency quasiperiodic, and chaotic self-oscillations are observed. The transitions to chaos occur as a result of a sequence of torus doubling bifurcations. When the control parameters are varied, the resonant limit cycles appear on a two-dimensional torus, and two-dimensional tori appear on a three-dimensional torus as a result of synchronization. We used a time series of dynamic variables, projections of phase portraits, Poincaré sections, and spectra of Lyapunov characteristic exponents to study the dynamics of the ring generator.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0057146