Numerical Method for Finding Synchronous Solutions of the Coupled Oscillator Networks

Shuai Wang (), Lu Wang () and Xue Yang ()
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Shuai Wang: Changchun University of Science and Technology
Lu Wang: Changchun University of Science and Technology
Xue Yang: Jilin University

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 1, No 9, 258-272

Abstract: 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.

Keywords: Synchronous solutions; Coupled oscillator networks; Optimization problem; Gauss–Newton method (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02282-5

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