Abstract
Two-frequency oscillations are the simplest case of quasiperiodic oscillations. In an autonomous regime, these oscillations are accompanied by the effect of mutual synchronization that corresponds to rational values of the Poincaré winding number. In this case synchronization regions are characterized by the so-called Arnold tongues, where the winding number Θ satisfies the condition Θ = m: n, with m and n positive integers.
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Notes
- 1.
A resonant two-dimensional torus is understood here as a partial resonance on a three-dimensional torus, when two of three independent frequencies become equal.
- 2.
From a qualitative point of view, these limit cycles are the images of invariant curves in the Poincaré section of the original system (14.2). In this connection, in what follows we will refer to these cycles as stable and unstable invariant curves.
- 3.
One must distinguish between the natural frequencies ω 1 and ω 2 of the autonomous oscillators, which are defined as the parameters of the system, and the frequencies ω 1 ′ and ω 2 ′ of the interacting oscillators.
- 4.
They represent the beat frequencies of the self-sustained oscillators in (14.2).
- 5.
The term ‘resonant torus’ is used here in the classical sense and characterizes the regime of a stable limit cycle on a torus.
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© 2014 Springer International Publishing Switzerland
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Anishchenko, V.S., Vadivasova, T.E., Strelkova, G.I. (2014). Synchronization of Two-Frequency Self-Sustained Oscillations. In: Deterministic Nonlinear Systems. Springer Series in Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-319-06871-8_14
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DOI: https://doi.org/10.1007/978-3-319-06871-8_14
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-06871-8
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