Traveling cluster pairs in a system of phase oscillators with positive and negative couplings under a periodic driving field

TL;DR

This paper numerically studies the clustering and traveling states of phase oscillators with mixed couplings under a periodic drive, revealing non-monotonic speed dependence and two traveling modes with distinct cluster dynamics.

Contribution

It demonstrates the existence of traveling cluster pairs and identifies symmetric and antisymmetric modes in a driven oscillator system with positive and negative couplings.

Findings

Traveling states occur under periodic driving similar to undriven systems.

Traveling speed varies non-monotonically with driving amplitude.

Two traveling modes: symmetric (same direction) and antisymmetric (opposite directions).

Abstract

We investigate numerically the clustering behavior of a system of phase oscillators with positive and negative couplings under a periodic external driving field with a bimodal distribution of driving phases. The phase distribution and the mean speed of the traveling state, as well as the order parameter for synchronization, are computed as the driving amplitude is varied. We observe that the periodically-driven system can also host traveling states for parameters in the same range as those for the case of a system without a driving field. The traveling speed is found to depend non-monotonically on the driving amplitude. In particular, oscillators divide into four clusters and move in pairs. Further, depending on the driving amplitude, two kinds of traveling mode arise: pairs of clusters traveling in the same direction (symmetric mode) and in opposite directions (antisymmetric mode). In the latter case (antisymmetric traveling mode), the average phase speed of the whole system apparently vanishes. A phenomenological argument for such behavior is given.