Remarks on the complete synchronization for the Kuramoto model with frustrations

Ha, Seung Yeal; Kim, Hwa Kil; Park, Jinyeong

doi:10.1142/s0219530517500130

Cited by 18 publications

(10 citation statements)

References 41 publications

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“…For the Kuramto model with heterogeneous frustrations with α kj , its emergent dynamics has been studied in [18]. 2.2.2.…”

Section: Previous Resultsmentioning

confidence: 99%

Emergent dynamics of the Lohe Hermitian sphere model with frustration

Ha,

Kang,

Park

2020

Preprint

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We study emergent dynamics of the Lohe hermitian sphere(LHS) model which can be derived from the Lohe tensor model [24] as a complex counterpart of the Lohe sphere(LS) model. The Lohe hermitian sphere model describes aggregate dynamics of point particles on the hermitian sphere HS d lying in C d+1 , and the coupling terms in the LHS model consist of two coupling terms. For identical ensemble with the same free flow dynamics, we provide a sufficient framework leading to the complete aggregation in which all point particles form a giant one-point cluster asymptotically. In contrast, for nonidentical ensemble, we also provide a sufficient framework for the practical aggregation. Our sufficient framework is formulated in terms of coupling strengths and initial data. We also provide several numerical examples and compare them with our analytical results.

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“…For the Kuramto model with heterogeneous frustrations with α kj , its emergent dynamics has been studied in [18]. 2.2.2.…”

Section: Previous Resultsmentioning

confidence: 99%

Emergent dynamics of the Lohe Hermitian sphere model with frustration

Ha,

Kang,

Park

2020

Preprint

Self Cite

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“…To the best knowledge of the authors, there is few work on the Kuramoto model over general digraph with frustration. The authors in [20] studied the Kuramoto model with frustrations on a complete graph which is a small perturbation of all-to-all network, and provided synchronization estimates in half circle.…”

Section: Introductionmentioning

confidence: 99%

Emergence of synchronization in Kuramoto model with frustration under general network topology

Zhu¹

2021

Preprint

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In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data is confined in half circle. As lack of uniform coercivity in general digraph, we apply the node decomposition criteria in [25] to capture a clear hierarchical structure, which successfully yields the dissipation mechanism of phase diameter and a small invariant set after finite time. Then the dissipation of frequency diameter will be clear, which eventually leads to the synchronization.

show abstract

“…To the best knowledge of the authors, there is few work on the Kuramoto model over general digraph with frustration. The authors in [18] studied the Kuramoto model with frustrations on a complete graph which is a small perturbation of all-to-all network, and provided synchronization estimates in half circle.…”

mentioning

confidence: 99%

Emergence of synchronization in Kuramoto model with frustration under general network topology

Zhu¹

2022

NHM

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<p style='text-indent:20px;'>In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data are confined in half circle. As lack of uniform coercivity in general digraph, we apply the node decomposition criteria in [<xref ref-type="bibr" rid="b25">25</xref>] to capture a clear hierarchical structure, which successfully yields the dissipation mechanism of phase diameter and an invariant set confined in quarter circle after some finite time. Then the dissipation of frequency diameter will be clear, which eventually leads to the synchronization.</p>

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Remarks on the complete synchronization for the Kuramoto model with frustrations

Cited by 18 publications

References 41 publications

Emergent dynamics of the Lohe Hermitian sphere model with frustration

Emergent dynamics of the Lohe Hermitian sphere model with frustration

Emergence of synchronization in Kuramoto model with frustration under general network topology

Emergence of synchronization in Kuramoto model with frustration under general network topology

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