Experimental evidence of explosive synchronization in mercury beating-heart oscillators

Kumar, Pawan; Verma, Dinesh Kumar; Parmananda, P.; Boccaletti, Stefano

doi:10.1103/physreve.91.062909

Cited by 57 publications

(30 citation statements)

References 21 publications

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“…Not only Ref. [437] gives evidence that a gradual increase of the coupling strength results in an abrupt and irreversible (first-order like) transition, but it also proved how to engineer magnetic-like states of synchronization, by the use of an external signal.…”

Section: Controlled Laboratory Experimentsmentioning

confidence: 99%

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Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization

et al. 2016

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Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous and reversible. Recently, however, explosive phenomena have been reported in complex networks' structure and dynamics, which rather remind first-order (discontinuous and irreversible) transitions. Explosive percolation, which was discovered in 2009, corresponds to an abrupt change in the network's structure, and explosive synchronization (which is concerned, instead, with the abrupt emergence of a collective state in the networks' dynamics) was studied as early as the first models of globally coupled phase oscillators were taken into consideration. The two phenomena have stimulated investigations and debates, attracting attention in many relevant fields. So far, various substantial contributions and progresses (including experimental verifications) have been made, which have provided insights on what structural and dynamical properties are needed for inducing such abrupt transformations, as well as have greatly enhanced our understanding of phase transitions in networked systems. Our intention is to offer here a monographic review on the main-stream literature, with the twofold aim of summarizing the existing results and pointing out possible directions for future research.

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Section: Controlled Laboratory Experimentsmentioning

confidence: 99%

“…Ref. [437] considered a star network configuration, where a central MBH oscillator is connected with other three MBH leaves oscillators. Furthermore, the experimental parameters are tuned properly, in a way that the natural frequencies of each oscillator is proportional to the number of its links.…”

Section: Controlled Laboratory Experimentsmentioning

confidence: 99%

Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization

et al. 2016

Self Cite

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“…Finally, it is also important to mention that the particular frequency assignment introduced by Gómez-Gardeñez et al [30] has been not only studied in networks of Kuramoto oscillators. In fact, the effects of degree-correlated frequencies were also investigated in networks made up of Rössler [247], FitzHughNagumo [250] and Stuart-Landau [276,277] oscillators, as well as in experiments with chemo-mechanical oscillators [278].…”

Section: Other Workmentioning

confidence: 99%

The Kuramoto model in complex networks

et al. 2016

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Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

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“…With the networks, further questions arise, e.g., what are the typical synchronization patterns or which types of network topologies can support AD or OD behavior. Important examples of chemical networks include BZ reactor systems, [22][23][24] BZ droplets, [25][26][27][28] BZ beads, [29][30][31][32][33] and chemomechanical 34 and electrochemical units. [35][36][37][38][39][40][41] Three globally coupled periodic oscillatory BZ reactors have been shown to exhibit the OD behavior.…”

Section: Introductionmentioning

confidence: 99%

Restoring oscillatory behavior from amplitude death with anti-phase synchronization patterns in networks of electrochemical oscillations

Nagao

Zou

Kurths

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The dynamical behavior of delay-coupled networks of electrochemical reactions is investigated to explore the formation of amplitude death (AD) and the synchronization states in a parameter region around the amplitude death region. It is shown that difference coupling with odd and even numbered ring and random networks can produce the AD phenomenon. Furthermore, this AD can be restored by changing the coupling type from difference to direct coupling. The restored oscillations tend to create synchronization patterns in which neighboring elements are in nearly anti-phase configuration. The ring networks produce frozen and rotating phase waves, while the random network exhibits a complex synchronization pattern with interwoven frozen and propagating phase waves. The experimental results are interpreted with a coupled Stuart-Landau oscillator model. The experimental and theoretical results reveal that AD behavior is a robust feature of delayed coupled networks of chemical units; if an oscillatory behavior is required again, even a small amount of direct coupling could be sufficient to restore the oscillations. The restored nearly anti-phase oscillatory patterns, which, to a certain extent, reflect the symmetry of the network, represent an effective means to overcome the AD phenomenon.

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Experimental evidence of explosive synchronization in mercury beating-heart oscillators

Cited by 57 publications

References 21 publications

Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization

Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization

The Kuramoto model in complex networks

Restoring oscillatory behavior from amplitude death with anti-phase synchronization patterns in networks of electrochemical oscillations

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