Dynamics and chaotic properties of the fully disordered Kuramoto model

TL;DR

This paper investigates the chaotic behavior and dynamics of the fully disordered Kuramoto model with random couplings, revealing the absence of frequency entrainment in large systems and widespread chaos across parameters.

Contribution

It provides the first extensive numerical and analytical analysis of chaos and dynamics in the disordered Kuramoto model, including formulas for frequency shifts and Lyapunov exponents.

Findings

Frequency entrainment does not occur in the thermodynamic limit.

Chaotic dynamics are widespread across parameter space.

Lyapunov exponent shows universal asymptotic behavior regardless of coupling asymmetry.

Abstract

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 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.