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Numerical Method for Finding Synchronous Solutions of the Coupled Oscillator Networks

Author

Listed:
  • Shuai Wang

    (Changchun University of Science and Technology)

  • Lu Wang

    (Changchun University of Science and Technology)

  • Xue Yang

    (Jilin University)

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.

Suggested Citation

  • Shuai Wang & Lu Wang & Xue Yang, 2023. "Numerical Method for Finding Synchronous Solutions of the Coupled Oscillator Networks," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 258-272, October.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:1:d:10.1007_s10957-023-02282-5
    DOI: 10.1007/s10957-023-02282-5
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    References listed on IDEAS

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    1. Z. X. Feng & X. Xu & S. G. Ji, 2009. "Finding the Periodic Solution of Differential Equation via Solving Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 75-86, October.
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