Communications in Mathematical Sciences
Volume 21 (2023)
Emergent behaviors of Kuramoto model with frustration under switching topology
Pages: 437 – 458
In this paper, we study the emergent behavior of Kuramoto model with switching topology under the effect of uniform frustration. In our frameworks, the switching interaction topology contains a spanning tree in any switching mode. For the initial configuration distributed in an open half circle, we first exploit a similar procedure in [T. Zhu, Netw. Heterog. Media, 17(2):255–291, 2022] to conclude that the Kuramoto oscillators will be pushed into a small region at some instant before the first network switching. Then in a large coupling and small frustration regime, we lift the Kuramoto model to the second-order formulation and apply the matrix theory-based approach in [J.-G. Dong, S.-Y. Ha and D. Kim, Anal. Appl., 19(2):305–342, 2021] to derive the exponential fast frequency synchronization.
synchronization, Kuramoto model, frustration, switching topology, spanning tree
2010 Mathematics Subject Classification
34C15, 34D06, 34K33, 93C15
The work of T. Zhu is supported by the Talent Fund of Hefei University, China (Grant no. 21-22RC23), by the National Natural Science Foundation of China (Grant no. 12201172), and by the Natural Science Foundation for Colleges and Universities in Anhui Province, China (Grant nos. 2022AH051790 and KJ2021A0996).
Received 21 August 2021
Received revised 14 May 2022
Accepted 6 June 2022
Published 1 February 2023