Complete synchrony under phase frustration in bi-harmonic Sakaguchi-Kuramoto networks

Determine whether there exists a specific configuration of intrinsic parameters—such as the coupling strengths K1 and K2 and the phase-lag parameters alpha and beta—in the Sakaguchi-Kuramoto model with bi-harmonic coupling that enforces complete synchronization (r = 1) despite phase frustration.

Background

The Sakaguchi-Kuramoto model introduces phase-lag parameters to account for interaction delays, but such phase frustration typically suppresses or prevents complete synchronization. In bi-harmonic extensions of the model, where both first and second harmonics contribute to coupling, the dynamics are richer but understanding of conditions for full synchrony is limited.

Prior studies often report that even small phase lags prohibit achieving r = 1, raising the problem of whether any precise tuning of model parameters could overcome this barrier. The paper frames this as a central open question motivating the development of an analytical approach to parameter and frequency assignment.