Print Email Facebook Twitter Synchronization of Coupled Phase Oscillators with Stochastic Disturbances and the Cycle Space of the Graph Title Synchronization of Coupled Phase Oscillators with Stochastic Disturbances and the Cycle Space of the Graph Author Xi, Kaihua (Shandong University) Wang, Zhen (Shandong University) Cheng, Aijie (Shandong University) Lin, H.X. (TU Delft Mathematical Physics) van Schuppen, J.H. (TU Delft Mathematical Physics) Zhang, Chenghui (Shandong University) Date 2023 Abstract The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine the fluctuations of phase differences in the lines between the nodes and to identify the vulnerable lines that may lead to desynchronization. The main result is the derivation of the asymptotic variance matrices of the phase differences which characterizes the severity of the fluctuations. It is found that the cycle space of the graph of the system plays a role in this characterization. With theory of the cycle space, the effect of forming small cycles on the fluctuations is evaluated. It is proven that adding a new line or increasing the coupling strength of a line affects the fluctuations in the lines in any cycle including this line, while it does not affect the fluctuations in the other lines. In particular, if the phase differences at the synchronous state are not changed by these actions, then the affected fluctuations reduce. Subject asymptotic variancecycle space of graphsinvariant probability distributionLyapunov equationnetworked systemstochastic Gaussian systemsynchronization stability To reference this document use: http://resolver.tudelft.nl/uuid:4974ab34-8a3a-437e-9881-4c8726c119c5 DOI https://doi.org/10.1137/22M1489502 ISSN 1536-0040 Source SIAM Journal on Applied Dynamical Systems, 22 (2), 1030-1052 Part of collection Institutional Repository Document type journal article Rights © 2023 Kaihua Xi, Zhen Wang, Aijie Cheng, H.X. Lin, J.H. van Schuppen, Chenghui Zhang Files PDF 22m1489502_1.pdf 1016.18 KB Close viewer /islandora/object/uuid:4974ab34-8a3a-437e-9881-4c8726c119c5/datastream/OBJ/view