Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions

Daido, Hiroaki

doi:10.1103/physrevlett.68.1073

Cited by 219 publications

(219 citation statements)

References 17 publications

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“…The special case k i = q i ≡ s i for all i was studied by H. Daido [7,8]. However, inspired by disordered spin systems, he admitted s i to be positive or negative.…”

Section: Synchronization Transition For Heterogeneous Couplingmentioning

confidence: 99%

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Synchronization of phase oscillators with heterogeneous coupling: A solvable case

Paissan

Zanette

2008

Physica D: Nonlinear Phenomena

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We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated to an oscillator, Kuramoto's theory for the transition to synchronization can be explicitly generalized, and the effects of coupling heterogeneity on synchronized states can be analytically studied. The two factors are respectively interpreted as the weight of the contribution of each oscillator to the mean field, and the coupling of each oscillator to that field. We explicitly analyze the effects of correlations between those weights and couplings, and show that synchronization can be completely inhibited when they are strongly anti-correlated. Numerical results validate the theory, but suggest that finite-size effect are relevant to the collective dynamics close to the synchronization transition, where oscillators become entrained in synchronized frequency clusters.

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“…The special case k i = q i ≡ s i for all i was studied by H. Daido [7,8]. However, inspired by disordered spin systems, he admitted s i to be positive or negative.…”

Section: Synchronization Transition For Heterogeneous Couplingmentioning

confidence: 99%

“…Open dots, on the other hand, stand for ensembles where the weights are drawn at random from a uniform distribution over the interval (0, 1), and then normalized to satisfy Eq. (8).…”

Section: Uncorrelated Couplings and Weightsmentioning

confidence: 99%

Synchronization of phase oscillators with heterogeneous coupling: A solvable case

Paissan

Zanette

2008

Physica D: Nonlinear Phenomena

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“…Example systems include pacemaker cells in the heart (Michaels et al, 1987), circadian cells in the brain (Liu et al, 1997), coupled cortical neurons (Crook et al, 1997), Hodgkin-Huxley neurons (Brown et al, 2003), brain networks (Varela et al, 2001), yeast cells (Ghosh et al, 1971), flashing fireflies (Buck, 1988;Ermentrout, 1991), chirping crickets (Walker, 1969), central pattern generators for animal locomotion (Kopell and Ermentrout, 1988), particle models mimicking animal flocking behavior (Ha et al, 2010b, and fish schools , among others. 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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“…When mixed positive and negative couplings are considered, the Kuramoto model can show a glass transition and can be also used to describe the neural networks [9][10][11] . For the former, the positive coupling denotes a ferromagnetic interaction while the negative coupling denotes an anti-ferromagnetic interaction.…”

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confidence: 99%

An efficient approach to suppress the negative role of contrarian oscillators in synchronization

Zhang

Ruan

Liu

2013

Chaos

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It has been found that contrarian oscillators usually take a negative role in the collective behaviors formed by conformist oscillators. However, experiments revealed that it is also possible to achieve a strong coherence even when there are contrarians in the system such as neuron networks with both excitable and inhibitory neurons. To understand the underlying mechanism of this abnormal phenomenon, we here consider a complex network of coupled Kuramoto oscillators with mixed positive and negative couplings and present an efficient approach, i.e. tit-for-tat strategy, to suppress the negative role of contrarian oscillators in synchronization and thus increase the order parameter of synchronization. Two classes of contrarian oscillators are numerically studied and a brief theoretical analysis is provided to explain the numerical results.

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Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions

Cited by 219 publications

References 17 publications

Synchronization of phase oscillators with heterogeneous coupling: A solvable case

Synchronization of phase oscillators with heterogeneous coupling: A solvable case

Synchronization in complex networks of phase oscillators: A survey

An efficient approach to suppress the negative role of contrarian oscillators in synchronization

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