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Numerical Method for Finding Synchronous Solutions of the Coupled Oscillator Networks

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Abstract

In this paper, we present a numerical method of finding synchronous solutions in coupled oscillator networks. We expand the optimization method of finding the periodic solution proposed by Feng et al. (J Optim Theory Appl 143:75-86, 2009) to find the synchronous solution in networks. The synchronous solutions here can be of many types, including in-phase synchronous solutions, anti-phase synchronous solutions, periodic synchronous solutions, cluster synchronous solutions, and so on. We show that the optimization problem in coupled oscillator networks can be regarded as a nonlinear least squares problem, so the corresponding Gauss–Newton method is proposed. Numerical simulations verify our results.

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Acknowledgements

We are very grateful to the anonymous referees for their valuable suggestions, which are very helpful to improve our manuscript. This work was supported by National Natural Science Foundation of China (No. 11901056), Natural Science Foundation of Jilin Province (20210101159JC) and the fund of the Department of Education of Jilin Province (JJKH20230789KJ).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun, 130000, China

    Shuai Wang & Lu Wang

  2. College of Mathematics, Jilin University, Changchun, 130000, China

    Xue Yang

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  1. Shuai Wang
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  2. Lu Wang
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  3. Xue Yang
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Correspondence to Shuai Wang.

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Communicated by Firdaus E. Udwadia.

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Wang, S., Wang, L. & Yang, X. Numerical Method for Finding Synchronous Solutions of the Coupled Oscillator Networks. J Optim Theory Appl 199, 258–272 (2023). https://doi.org/10.1007/s10957-023-02282-5

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