# Oscillators that sync and swarm

## TL;DR

This paper introduces 'swarmalators', systems where oscillators synchronize their phases while moving through space, revealing five possible collective states with applications in biological and physical systems.

## Contribution

It proposes a coupled phase and spatial dynamics model called swarmalators, and predicts five distinct long-term collective states.

## Key findings

- Five collective states predicted by the model
- Applicable to biological systems like sperm and frogs
- Potential observations in colloidal suspensions

## Abstract

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact.