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.