Kuramoto Model of Coupled Oscillators with Positive and Negative Coupling Parameters: An Example of Conformist and Contrarian Oscillators

Hong, Hyunsuk; Strogatz, Steven H.

doi:10.1103/physrevlett.106.054102

Cited by 373 publications

(410 citation statements)

References 27 publications

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“…Additionally, the inclusion of odd coupling functions possibly with higher-order harmonics can lead to qualitatively different behavior and scaling laws as discussed by Daido (1994);Crawford (1995);Strogatz (2000). Finally, a topic of recent interest is mixed attractive and repulsive coupling (Hong and Strogatz, 2011;El Ati and Panteley, 2013b;Burylko, 2012).…”

Section: Conclusion and Open Research Directionsmentioning

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: Conclusion and Open Research Directionsmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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“…Actually, we employ the extended approach [8] where the coupling between oscillators is determined by a symmetric matrix M m,n ≡ f (v m , v n ) instead of a constant gain factor K. Hence, the phases θ m of the oscillators evolve according to the following update rule:…”

Section: Transfer To Network Of Coupled Kuramoto Oscillatorsmentioning

confidence: 99%

“…Similar features have a positive compatibility, therefore the corresponding oscillators phase-lock and form a perceptual group, which repels dissimilar features by means of negative couplings. The Kuramoto model has been investigated in many variations [8,9] and we refer the interested reader to this work.…”

Section: Introductionmentioning

confidence: 99%

Perceptual grouping through competition in coupled oscillator networks

2014

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Abstract. In this paper we present a novel approach to model perceptual grouping based on phase and frequency synchronization in a network of coupled Kuramoto oscillators. Transferring the grouping concept from the Competitive Layer Model (CLM) to a network of Kuramoto oscillators, we preserve the excellent grouping capabilities of the CLM, while dramatically improving the convergence rate, robustness to noise, and computational performance, which is verified in a series of artificial grouping experiments.

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“…We performed experiments and simulations with the conformist/contrarian system [104,105]. In experiments we systematically observed amplitude di↵erences between the conformists and the contrarians when order emerged in the subpopulations.…”

Section: Radial E↵ects In the Conformist/contrarian Systemmentioning

confidence: 99%

“…The behavior of a population of phase oscillators with a mixture of positive and negative mean field coupling is described by [104,105] (s)…”

Section: Theorymentioning

confidence: 99%

Improving Reduced Variable Models for Complex Systems via Experiment

Blaha

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Populations of simple interacting oscillators can give rise to complex dynamics.Real-world examples of such systems abound in biology, chemistry, and physics.Reduced-variable models can describe these systems. The phase model is a particularly successful reduced-variable model which, in its simplest form, each element is represented by one variable, the phase of oscillation. The phase model can be constructed from observable variables, without specific knowledge of underlying phenomenological behavior. Such reduced variable models are easier to construct and more generalizable than models derived from underlying physics or chemistry.In this dissertation, we study the dynamics of a population of coupled electrochemical oscillators in order to modify the phase model to expand its applicability.Specifically, we develop a two-phase model, a phase and radius model, and models with network coupling.We analyze data from two coupled oscillators with a standard one-dimensional phase model and a newer two-dimensional phase model. The same quantity of data is needed for either model. The two-dimensional analysis reveals behaviors and coupling parameters in theoretical and experimental examples that the onedimensional analysis does not show. The two-dimensional model could be useful in systems that exhibit learning due to its ability to distinguish stimulation and reaction. We extend the Stuart-Landau model to describe clustering dynamics for higher harmonic oscillators. We present examples of asymmetrical clusters arising from networks of higher harmonic oscillators. We show that the amplitude of oscillation is functionally influenced by coupling; we believe this "amplitude coupling function" has not been previously described. This function can be constructed from the original time series with no additional measurements.Recently, combined phase and amplitude models have gained attention; we explore the conditions where a phase and amplitude model is useful. We show experimentally a change in cluster state due only to changes in coupling strength. Such a transition is not possible with a phase-only model. Simulations with the extended Stuart-Landau model match experimental results. We demonstrate a method for predicting the amplitude coupling function from the coupling. Prior to this study, the relationship between stimulation and response was not known for the amplitude. We suggest that the phase and amplitude model will be most useful (1) in modeling high-harmonic oscillations, and (2) where coupling exceeds the "weak coupling" approximation of the phase-only model. iv

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Kuramoto Model of Coupled Oscillators with Positive and Negative Coupling Parameters: An Example of Conformist and Contrarian Oscillators

Cited by 373 publications

References 27 publications

Synchronization in complex networks of phase oscillators: A survey

Synchronization in complex networks of phase oscillators: A survey

Perceptual grouping through competition in coupled oscillator networks

Improving Reduced Variable Models for Complex Systems via Experiment

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