Physics of the rhythmic applause

Néda, Zoltán; Ravasz, E.; Vicsek, Tamás; Bréchet, Y.; Barabási, Albert László

doi:10.1103/physreve.61.6987

Cited by 241 publications

(183 citation statements)

References 13 publications

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“…The coupled oscillator model (1) also appears in physics and chemistry in modeling and analysis of spin glass models (Daido, 1992;Jongen et al, 2001), flavor evolution of neutrinos (Pantaleone, 1998), coupled Josephson junctions (Wiesenfeld et al, 1998), coupled metronomes (Pantaleone, 2002), Huygen's coupled pendulum clocks (Bennett et al, 2002;Kapitaniak et al, 2012), micromechanical oscillators with optical (Zhang et al, 2012) or mechanical (Shim et al, 2007) coupling, and in the analysis of chemical oscillations (Kuramoto, 1984a;Kiss et al, 2002). Finally, oscillator networks of the form (1) also serve as phenomenological models for synchronization phenomena in social networks, such as rhythmic applause (Néda et al, 2000), opinion dynamics (Pluchino et al, 2006a,b), pedestrian crowd synchrony on London's Millennium bridge , and decision making in animal groups (Leonard et al, 2012).…”

Section: Applications In Sciencesmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.

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Section: Applications In Sciencesmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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“…Examples include flashing of fireflies [5], applauding persons [6], systems describing circadian rhythms in animals [7], Josephson junction arrays [8], moving pedestrians on footbridges [9] and many more [10]. Mathematical modeling of these complex systems often involves the important steps of capturing dynamics of the interacting units by nonlinear oscillators and interaction by suitable coupling functions [11].…”

Section: Introductionmentioning

confidence: 99%

Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model

et al. 2017

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We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order parameter for the model in the thermodynamic limit. Using the self-consistent equations we investigate transition to synchronization in SK model on uncorrelated scale-free (SF) and Erdős-Rényi (ER) networks in detail. Depending on the degree distribution exponent (γ) of SF networks and phase-frustration parameter, the population undergoes from first order transition (explosive synchronization (ES)) to second order transition and vice versa. In ER networks transition is always second order irrespective of the phase-lag parameter. We observe that the critical coupling strength for the onset of synchronization is decreased by phase-frustration parameter in case of SF network where as in ER network, the phase-frustration delays the onset of synchronization. Extensive numerical simulations using SF and ER networks are performed to validate the analytical results. An analytical expression of critical coupling strength for the onset of synchronization is also derived from the self consistent equations considering the vanishing order parameter limit.

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“…This many-body cooperative effect is observed in many physical and biological systems, pervading length and time scales of several orders of magnitude. Some examples are metabolic synchrony in yeast cell suspensions [1], synchronized firings of cardiac pacemaker cells [2], flashing in unison by groups of fireflies [3], voltage oscillations at a common frequency in an array of current-biased Josephson junctions [4], phase synchronization in electrical power distribution networks [5][6][7], rhythmic applause [8], animal flocking behavior [9]; see Ref. [10] for a recent survey.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium first-order phase transition in coupled oscillator systems with inertia and noise

2014

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We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a general unimodal frequency distribution, we report here the complete phase diagram of the model in the space of dimensionless moment of inertia, temperature, and width of the frequency distribution. We demonstrate that the system undergoes a nonequilibrium first-order phase transition from a synchronized phase at low parameter values to an incoherent phase at high values. We provide strong numerical evidence for the existence of both the synchronized and the incoherent phase, treating the latter analytically to obtain the corresponding linear stability threshold that bounds the first-order transition point from below. In the limit of zero noise and inertia, when the dynamics reduces to the one of the Kuramoto model, we recover the associated known continuous transition. At finite noise and inertia but in the absence of natural frequencies, the dynamics becomes that of a well-studied model of long-range interactions, the Hamiltonian mean-field model. Close to the first-order phase transition, we show that the escape time out of metastable states scales exponentially with the number of oscillators, which we explain to be stemming from the long-range nature of the interaction between the oscillators.

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Physics of the rhythmic applause

Cited by 241 publications

References 13 publications

Synchronization in complex networks of phase oscillators: A survey

Synchronization in complex networks of phase oscillators: A survey

Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model

Nonequilibrium first-order phase transition in coupled oscillator systems with inertia and noise

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