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

Tingting Zhu; Tingting Zhu

doi:10.3934/nhm.2022005

Networks and Heterogeneous Media

2022, Volume 17, Issue 2: 255-291. doi: 10.3934/nhm.2022005

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

Tingting Zhu

Key Laboratory of Applied Mathematics and Artificial Intelligence Mechanism, Hefei University, Hefei 230601, China

Received: 01 August 2021 Revised: 01 December 2021 Published: 22 February 2022
Primary: 34D06, 34C15; Secondary: 92B25, 70F99

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 [25] 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.
- Kuramoto model,
- frustration,
- general digraph,
- spanning tree,
- hypo-coercivity,
- synchronization
Citation: Tingting Zhu. Emergence of synchronization in Kuramoto model with frustration under general network topology[J]. Networks and Heterogeneous Media, 2022, 17(2): 255-291. doi: 10.3934/nhm.2022005

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Abstract

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 [25] 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.

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