Journal ArticleDOI
Bifurcational mechanisms of synchronization of a resonant limit cycle on a two-dimensional torus
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TLDR
It is shown that the resonant limit cycle can be generally synchronized on the torus through the resonance destruction followed by the locking of one and then another one of the basic frequencies.Abstract:
We study synchronization of a resonant limit cycle on a two-dimensional torus with an external harmonic signal. The regime of the resonant limit cycle is realized in a system of two coupled Van der Pol oscillators; we consider the resonances 1:1 and 1:3. We analyze the influence of coupling strength between the oscillators. We show that the resonant limit cycle can be generally synchronized on the torus through the resonance destruction followed by the locking of one and then another one of the basic frequencies. We consider the bifurcational mechanism of the synchronization effect.read more
Citations
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Introduction to Focus Issue: Synchronization in Complex Networks
TL;DR: This interdisciplinary oriented Focus Issue presents recent progress in synchronization in large ensembles of coupled interacting units with contributions on generic methods, specific model studies, and applications.
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Synchronization and multi-frequency oscillations in the low-dimensional chain of the self-oscillators
TL;DR: In this article, the problem of growing complexity of the dynamics of the coupled phase oscillators as the number of oscillators in the chain increases is considered and the organization of the parameter space (parameter of the frequency detuning between the second and the first oscillators versus parameter of dissipative coupling) is discussed.
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Forced synchronization of quasiperiodic oscillations in a thermoacoustic system
TL;DR: In this article, the authors experimentally examined the effect of periodic acoustic forcing on a prototypical thermoacoustic system consisting of a ducted laminar premixed flame oscillating quasiperiodically.
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About Landau–Hopf scenario in a system of coupled self-oscillators
TL;DR: In this paper, the conditions for which an ensemble of interacting oscillators may demonstrate the Landau-Hopf scenario of successive birth of multi-frequency quasi-periodic motions are discussed.
Journal ArticleDOI
Forced synchronization of quasiperiodic oscillations
Nataliya Stankevich,Nataliya Stankevich,Jürgen Kurths,Jürgen Kurths,Alexander P. Kuznetsov,Alexander P. Kuznetsov +5 more
TL;DR: This work analyzes synchronization when the autonomous generator demonstrates periodic, quasiperiodic, respective weakly chaotic oscillations, and a partial destruction of this features and of the regime of three-frequency tori are found.
References
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On the nature of turbulence
David Ruelle,Floris Takens +1 more
TL;DR: A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed in this article, where the authors propose a mechanism for generating turbulence in a dissipative system with respect to dissipative energy.
Journal ArticleDOI
Occurrence of strange axiom a attractors near quasi periodic flows on tm, m is greater than or equal to 3
TL;DR: In this article, it was shown that by a smallC 2 ∞ perturbation of a quasiperiodic flow on the 3-torus (m>3), one can produce strange AxiomA attractors.
Journal ArticleDOI
Bifurcations of tori and phase locking in a dissipative system of differential equations
TL;DR: In this article, a two-dimensional torus undergoes first two period-doubling bifurcations and then a transition to a strange attractor, characterized by a power spectrum which retains the two fundamental frequencies of the original torus superimposed on a broad, jagged background.
Journal ArticleDOI
Winding number locking on a two-dimensional torus: Synchronization of quasiperiodic motions
TL;DR: A new autonomous dynamical system of dimension N = 4 is proposed that demonstrates the regime of stable two-frequency motions and period-doubling bifurcations of a two-dimensional torus.