Binary Mixtures of Locally Coupled Mobile Oscillators

TL;DR

This paper investigates synchronization in binary mixtures of mobile Kuramoto oscillators in 2D, revealing how mobility, coupling, and mixture composition influence phase coherence and synchronization times.

Contribution

It introduces two models of locally coupled mobile oscillators with distinct phase interaction rules and analyzes their synchronization behavior and stability.

Findings

Synchronization attractors are robust in model I regardless of mixture composition.

Synchronization time decreases with increased mobility and neighbor exchange.

Model J shows suppression of synchronization in one subpopulation and emergence in the other under certain couplings.

Abstract

We study synchronization dynamics in binary mixtures of locally coupled Kuramoto oscillators which perform Brownian motion in a two-dimensional box. We introduce two models, where in model $\cal I$ there are two type of oscillators, say $\cal A$ and $\cal B$, and any two similar oscillators tend to synchronize their phases, while any two dissimilar ones tend to be out of phase. In model $\cal J$, in contrast, the oscillators in subpopulation $\cal A$ behave as in model $\cal I$, while the oscillators in subpopulation $\cal B$ tend to be out of phase with all the others. In the real space all the oscillators in both models interact via a soft-core repulsive potential. Both subpopulations of model $\cal I$ and subpopulation $\cal A$ of model $\cal J$, by their own, exhibit a phase coherent attractor in a certain region of model parameters. The approach to the attractor, after an initial transient regime, is exponential with some characteristic synchronization time scale $\tau$. Numerical analysis reveals that the attractors of the two subpopulations survive within model $\cal I$, regardless of the composition of the mixture $\phi$ and the strength of the cross-population negative coupling constant $H$, and that $\tau$ sensitively depends on $\phi$, $H$ and the packing fraction. In particular, the ability of the oscillators to move and exchange neighbours can significantly decrease $\tau$. In contrast, model $\cal J$ predicts suppression of the synchronized state in subpopulation $\cal A$ and emergence of the coherent attractor in the "contrarians" subpopulation $\cal B$ for strong and weak cross-population coupling, respectively.