Synchronization of the generalized Kuramoto model with time delay and frustration

Tingting Zhu; Tingting Zhu

doi:10.3934/nhm.2023077

Networks and Heterogeneous Media

2023, Volume 18, Issue 4: 1772-1798. doi: 10.3934/nhm.2023077

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Research article

Synchronization of the generalized Kuramoto model with time delay and frustration

Tingting Zhu ^{1,2
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1.
School of Artificial Intelligence and Big Data, Hefei University, Hefei 230601, China
2.
Key Laboratory of Applied Mathematics and Artificial Intelligence Mechanism, Hefei University, Hefei 230601, China

Received: 20 May 2023 Revised: 17 September 2023 Accepted: 09 October 2023 Published: 18 October 2023

We studied the collective behaviors of the time-delayed Kuramoto model with frustration under general network topology. For the generalized Kuramoto model with the graph diameter no greater than two and under a sufficient regime in terms of small time delay and frustration and large coupling strength, we showed that the complete frequency synchronization occurs exponentially fast when the initial configuration is distributed in a half circle. We also studied a complete network, which is a small perturbation of all-to-all coupling, as well as presented sufficient frameworks leading to the exponential emergence of frequency synchronization for the initial data confined in a half circle.
- Kuramoto model,
- frequency synchronization,
- time delay,
- frustration,
- general network topology
Citation: Tingting Zhu. Synchronization of the generalized Kuramoto model with time delay and frustration[J]. Networks and Heterogeneous Media, 2023, 18(4): 1772-1798. doi: 10.3934/nhm.2023077

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Abstract

We studied the collective behaviors of the time-delayed Kuramoto model with frustration under general network topology. For the generalized Kuramoto model with the graph diameter no greater than two and under a sufficient regime in terms of small time delay and frustration and large coupling strength, we showed that the complete frequency synchronization occurs exponentially fast when the initial configuration is distributed in a half circle. We also studied a complete network, which is a small perturbation of all-to-all coupling, as well as presented sufficient frameworks leading to the exponential emergence of frequency synchronization for the initial data confined in a half circle.

References

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