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We consider a mean-field model of coupled phase oscillators with quenched disorder in the coupling strengths and natural frequencies. When these two kinds of disorder are uncorrelated (and when the positive and negative couplings are equal in number and strength), it is known that phase coherence cannot occur and synchronization is absent. Here we explore the effects of correlating the disorder. Specifically, we assume that any given oscillator either attracts or repels all the others, and that the sign of the interaction is deterministically correlated with the given oscillator's natural frequency. For symmetrically correlated disorder with zero mean, we find that the system spontaneously synchronizes, once the width of the frequency distribution falls below a critical value. For asymmetrically correlated disorder, the model displays coherent traveling waves: the complex order parameter becomes nonzero and rotates with constant frequency different from the system's mean natural frequency. Thus, in both cases, correlated disorder can trigger phase coherence. [ABSTRACT FROM AUTHOR]

We study a simple model of swarmalators subject to periodic forcing and confined to moving around a one-dimensional ring. This is a toy model for physical systems with a mix of sync, swarming, and forcing, such as colloidal micromotors. We find rich behavior: pinned states where the swarmalators are locked to the driving, sync states where their phases are either identical or have fixed differences, and unsteady states, such as swarmalator chimera where the population splits into two sync dots enclosed by a "train" of swarmalators that run around a peanut-shaped loop. We derive the stability thresholds for most of these states which give us a good approximation of the model's phase diagram.

We study a population of swarmalators, mobile variants of phase oscillators, which run on a ring and have both attractive and repulsive interactions. This one-dimensional (1D) swarmalator model produces several of collective states: the standard sync and async states as well as a splaylike "polarized" state and several unsteady states such as active bands or swirling. The model's simplicity allows us to describe some of the states analytically. The model can be considered as a toy model for real-world swarmalators such as vinegar eels and sperm which swarm in quasi-1D geometries.