Topological transitions in swarmalators systems

TL;DR

This paper explores how topological changes govern the transitions in swarmalator systems, providing a new topological framework to understand collective behavior shifts.

Contribution

It introduces a topological approach to analyze swarmalator dynamics, focusing on topological charge and helicity to explain observed transitions.

Findings

Transitions are linked to changes in topological charge and helicity.

The topological framework clarifies synchronization phenomena.

Topological measures predict system behavior shifts.

Abstract

After its development, the swarmalators model attracted a great deal of attention since it was found to be very suitable to reproduce several behaviors in collective dynamics. However, few works explain the transitions that are observed while varying system parameters. In this letter, we demonstrate that the changes observed in swarmalator dynamics are governed by changes in the system's topology. To provide a deeper understanding of these changes, we present a topological framework for the swarmalator system and determine the topological charge $Q$ and the helicity $\gamma$ of the corresponding topology. Investigations on synchronization and transition to synchronization are studied using this topological charge and the variance of the helicity.