Exponential synchronization of finite-dimensional Kuramoto model at critical coupling strength

Choi, Young Pil; Ha, Seung Yeal; Kang, Myeongmin; Kang, Myungjoo

doi:10.4310/cms.2013.v11.n2.a3

Cited by 13 publications

(4 citation statements)

References 26 publications

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“…, n − 1}, and for any of its permutations. In recent work, (Choi et al, 2013) show that the bipolar distribution ω bip is the unique worst-case distribution, where synchronization fails for K = K critical .…”

Section: Exact and Implicit Conditionsmentioning

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: Exact and Implicit Conditionsmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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“…This gives exactly the same assumptions for the complete frequency synchronization estimate in [5]. We refer to [2,6,10,11,12] for the complete frequency synchronization estimate in the case of non time delayed interactions.…”

Section: Let Us Denotementioning

confidence: 83%

Exponential synchronization of Kuramoto oscillators with time delayed coupling

Choi¹,

Pignotti²

2019

Preprint

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We discuss the asymptotic frequency synchronization for the non-identical Kuramoto oscillators with time delayed interactions. We provide explicit lower bound on the coupling strength and upper bound on the time delay in terms of initial configurations ensuring exponential synchronization. This generalizes not only the frequency synchronization estimate by Choi et al. [Physica D, 241, (2012), 735-754] for the non-identical Kuramoto oscillators without time delays but also improves previous result by Schmidt et al. [Automatica, 48, (2012), 3008-3017] in the case of homogeneous time delays where the initial phase diameter is assumed to be less than π/2. The proof relies on a Lyapunov functional approach.

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“…This gives exactly the same assumptions for the complete frequency synchronization estimate in [5]. We refer to [2,6,[11][12][13] for the complete frequency synchronization estimate in the case of non-time-delayed interactions.…”

Section: Introductionmentioning

confidence: 83%

Exponential synchronization of Kuramoto oscillators with time delayed coupling

Choi

Pignotti

2021

Communications in Mathematical Sciences

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We discuss the asymptotic frequency synchronization for the non-identical Kuramoto oscillators with time delayed interactions. We provide explicit lower bound on the coupling strength and upper bound on the time delay in terms of initial configurations ensuring exponential synchronization. This generalizes not only the frequency synchronization estimate by Choi et al. [Phys. D, 241(7):735-754, 2012] for the non-identical Kuramoto oscillators without time delays but also improves previous result by Schmidt et al. [Automatica, 48(12):3008-3017, 2012] in the case of homogeneous time delays where the initial phase diameter is assumed to be less than π/2. The proof relies on a Lyapunov functional approach.

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Exponential synchronization of finite-dimensional Kuramoto model at critical coupling strength

Cited by 13 publications

References 26 publications

Synchronization in complex networks of phase oscillators: A survey

Synchronization in complex networks of phase oscillators: A survey

Exponential synchronization of Kuramoto oscillators with time delayed coupling

Exponential synchronization of Kuramoto oscillators with time delayed coupling

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