Abstract
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.
Highlights
As a universal concept in nonlinear science, synchronization has been widely observed in both natural and manmade systems [1]
To confirm the experimental findings, we study irrational phase synchronization (IPS) using numerical simulations based on a simplified model
If the phase difference Δrφ gradually approaches 0 as r approaches the irrational ratio r1, one can conclude that at r1, the two metronomes achieve the state of IPS [16]
Summary
As a universal concept in nonlinear science, synchronization has been widely observed in both natural and manmade systems [1]. Because only the phases of the oscillators are correlated, phase synchronization represents a weaker type of coherent motion than complete synchronization and is typically observed at a lower coupling strength than the latter. The numerical discovery of IPS represents a significant extension to the current knowledge of phase synchronization, as it is common sense that for coupled periodic oscillators, the resonance tongues that correspond to the irrational frequency ratios are of zero measure. By coupling two nonidentical periodic metronomes, we demonstrate that IPS is, observable in realistic systems. [20], it is shown that by varying the coupling strength and the frequency mismatch, the metronomes can achieve phase or envelope synchronization. To validate the experimental findings, we gradually vary the natural frequency of the second metronome from 152 to 168 BPM and investigate the synchronization behaviors of the two phases. According to Ref. [16], given that r is continuously varying over some interval of the parameter space, IPS can always be achieved through careful tuning of the parameter within this interval
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