Numerical Method for Finding Synchronous Solutions of the Coupled Oscillator Networks

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.

Automated summary

In this paper, a numerical method is presented for finding synchronous solutions in coupled oscillator networks. The optimization method proposed by Feng et al. (2009) for finding periodic solutions is expanded to find synchronous solutions in networks. The optimization problem in coupled oscillator networks is shown to be a nonlinear least squares problem, and a corresponding Gauss-Newton method is proposed. Numerical simulations confirm the results.