Breaking of time translation invariance in a deterministic system of Kuramoto oscillators

Physical aging has been observed in systems with stochastic thermal fluctuations like spin glasses and colloids. This phenomenon has also been detected in a system of repulsively coupled Kuramoto oscillators under the effect of an external noise, where the noise played the role of the thermal fluctuations in spin glasses. In this study we consider fully deterministic systems of repulsively coupled Kuramoto oscillators on hexagonal lattices of different sizes with different characteristics of the rich attractor space. A disorder is introduced in the system trough a random and regular distribution of natural frequencies of individual oscillators. We find the breaking of time-translation invariance in the system caused by long transient times. This feature disappears in the regime with weaker negative coupling between the oscillators in the vicinity of the transition point to the monostable state (positive coupling), where we do not find any stable periodic orbits but only irregular phase trajectories.