Experimental study on synchronization of three coupled mechanical metronomes

Hu, Qiang; Liu, Weiqing; Yang, Han; Xiao, Jinghua; Qian, Xiaolan

doi:10.1088/0143-0807/34/2/291

Cited by 10 publications

(14 citation statements)

References 26 publications

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“…Nevertheless, frustration plays an important role in the dynamics of three-coupled oscillators5, because it may cause symmetry breaking that drives certain asymmetric synchronised modes6. Earlier studies have demonstrated that several non-trivial mode patterns were observed in three-coupled oscillators of physical78910, chemical11, and biological systems121314 as well as human group dynamics15. Since the symmetry-based understanding is model independent, it is expected to hold for synchronisation of three-coupled candle flames.…”

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confidence: 99%

Synchronization in flickering of three-coupled candle flames

Okamoto

Kijima

Umeno

et al. 2016

Sci Rep

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When two or more candle flames are fused by approaching them together, the resulting large flame often exhibits flickering, i.e., prolonged high-frequency oscillation in its size and luminance. In the present work, we investigate the collective behaviour of three-coupled candle flame oscillators in a triangular arrangement. The system showed four distinct types of syncronised modes as a consequence of spontaneous symmetry breaking. The modes obtained include the in-phase mode, the partial in-phase mode, the rotation mode, and an anomalous one called the “death” mode that causes a sudden stop of the flame oscillation followed by self-sustained stable combustion. We also clarified the correlation between the inter-flame distance and the frequency with which the modes occur.

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confidence: 99%

Synchronization in flickering of three-coupled candle flames

Okamoto

Kijima

Umeno

et al. 2016

Sci Rep

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“…2(a-c). the feature of SS [16]. In addition, the audio signals of the upper metronomes, which have the reduced intensity, can be straightforwardly distinguished from that of the lower metronomes.…”

Section: Resultsmentioning

confidence: 97%

“…By coupling three identical pendulums, Czolczynski et al observed the splay synchronization (SS) state where the phase difference between any two pendulums is fixed at 2π/3. By a CCD acquisition system, Hu et al confirmed this SS state in experiment [16]. By the same acquisition system, Jia et al successfully generated in experiment the triplet synchronization state predicted theoretically by Kralemann et al [17,18].…”

Section: Introductionmentioning

confidence: 78%

“…In Ref. [16], the authors developed a sophisticated CCD acquisition system to detect the SS state, which is able to measure the synchronization relationship among the metronomes with a high precision [17]. Similar video-based techniques have been used in detecting the collective behavior of an ensemble of coupled metronomes [21,23].…”

Section: Experimental Setup and Measure Techniquementioning

confidence: 99%

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Synchronization of coupled metronomes on two layers

Zhang

Wang

2017

Front. Phys.

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Coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of complex dynamical systems, as well as a classical setup for classroom demonstrations of synchronization phenomena. Whereas previous studies of metronome synchronization have been concentrating on symmetric coupling schemes, here we consider the asymmetric case by adopting the scheme of layered metronomes. Specifically, we place two metronomes on each layer, and couple two layers by placing one on top of the other. By varying the initial conditions of the metronomes and adjusting the friction between the two layers, a variety of synchronous patterns are observed in experiment, including the splay synchronization (SS) state, the generalized splay synchronization (GSS) state , the anti-phase synchronization (APS) state, the in-phase delay synchronization (IPDS) state, and the in-phase synchronization (IPS) state. In particular, the IPDS state, in which the metronomes on each layer are synchronized in phase but are of a constant phase delay to metronomes on the other layer, is observed for the first time. In addition, a new technique based on audio signals is proposed for pattern detection, which is more convenient and easier to apply than the existing acquisition techniques. Furthermore, a theoretical model is developed to explain the experimental observations, and is employed to explore the dynamical properties of the patterns, including the basin distributions and the pattern transitions. Our study sheds new lights on the collective behaviors of coupled metronomes, and the developed setup can be used in the classroom for demonstration purposes.Comment: 19 pages, 6 figure

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“…The metronome device was initially designed by Zou et al in Ref. [ 19 ] and was later improved on by several other researchers [ 20 , 21 ]. In Ref.…”

Section: Materials and Experimental Resultsmentioning

confidence: 99%

Experimental Study of the Irrational Phase Synchronization of Coupled Nonidentical Mechanical Metronomes

Song

Liu

et al. 2015

PLoS ONE

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It has recently been observed in numerical simulations that the phases of two coupled nonlinear oscillators can become locked into an irrational ratio, exhibiting the phenomenon of irrational phase synchronization (IPS) [Phys. Rev. E 69, 056228 (2004)]. Here, using two coupled nonidentical periodic mechanical metronomes, we revisit this interesting phenomenon through experimental studies. It is demonstrated that under suitable couplings, the phases of the metronomes indeed can become locked into irrational ratios. Numerical simulations confirm the experimental observations and also reveal that in the IPS state, the system dynamics are chaotic. Our studies provide a solid step toward further studies of IPS.

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Experimental study on synchronization of three coupled mechanical metronomes

Cited by 10 publications

References 26 publications

Synchronization in flickering of three-coupled candle flames

Synchronization in flickering of three-coupled candle flames

Synchronization of coupled metronomes on two layers

Experimental Study of the Irrational Phase Synchronization of Coupled Nonidentical Mechanical Metronomes

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