Increasing the synchronization stability in complex networks

Journal Article (2023)
Author(s)

Xian Wu (Shandong University)

Kaihua Xi (Shandong University)

Aijie Cheng (Shandong University)

Haixiang Lin (TU Delft - Mathematical Physics)

J.H. van Schuppen (TU Delft - Mathematical Physics)

Research Group
Mathematical Physics
Copyright
© 2023 Xian Wu, Kaihua Xi, Aijie Cheng, H.X. Lin, J.H. van Schuppen
DOI related publication
https://doi.org/10.1063/5.0114974
More Info
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Publication Year
2023
Language
English
Copyright
© 2023 Xian Wu, Kaihua Xi, Aijie Cheng, H.X. Lin, J.H. van Schuppen
Research Group
Mathematical Physics
Issue number
4
Volume number
33
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Abstract

We aim to increase the ability of coupled phase oscillators to maintain synchronization when the system is affected by stochastic disturbances. We model the disturbances by Gaussian noise and use the mean first hitting time when the state hits the boundary of a secure domain, that is a subset of the basin of attraction, to measure synchronization stability. Based on the invariant probability distribution of a system of phase oscillators subject to Gaussian disturbances, we propose an optimization method to increase the mean first hitting time and, thus, increase synchronization stability. In this method, a new metric for synchronization stability is defined as the probability of the state being absent from the secure domain, which reflects the impact of all the system parameters and the strength of disturbances. Furthermore, by this new metric, one may identify those edges that may lead to desynchronization with a high risk. A case study shows that the mean first hitting time is dramatically increased after solving corresponding optimization problems, and vulnerable edges are effectively identified. It is also found that optimizing synchronization by maximizing the order parameter or the phase cohesiveness may dramatically increase the value of the metric and decrease the mean first hitting time, thus decrease synchronization stability.

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