2026/04/12 by Arkady Pikovsky · 1 voice
Physics and Astronomy · #nlin.AO
The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking into account a phase shift in coupling. In the thermodynamic limit, we derive dependencies of the order parameters on the coupling strength and the phase shift, and describe two transitions from disorder to partial synchrony and from partial synchrony to complete synchrony. In all cases, the first transition is discontinuous, although for phase shifts close to π/2, the jump is exponentially small.