Dynamics and chaotic properties of the fully disordered Kuramoto model

Frustrated random interactions are a key ingredient of spin glasses. From this perspective, we study the dynamics of the Kuramoto model with quenched random couplings: the simplest oscillator ensemble with fully disordered interactions. We answer some open questions by means of extensive numerical simulations and a perturbative calculation (the cavity method). We show that frequency entrainment is not realized in the thermodynamic limit and that chaotic dynamics are pervasive in parameter space. In the weak coupling regime, we find closed formulas for the frequency shift and the dissipativeness of the model. Interestingly, the largest Lyapunov exponent is found to exhibit the same asymptotic dependence on the coupling constant irrespective of the coupling asymmetry, within the numerical accuracy.