Expected and unexpected routes to synchronization in a system of swarmalators

TL;DR

This paper explores the diverse synchronization behaviors of swarmalators, revealing how different frequency distributions lead to various phase transitions, including first-order, second-order, and novel cluster-switching phenomena.

Contribution

It introduces new synchronization states and transitions in swarmalator systems, including the Rotational Splintered Phase Wave state, expanding understanding of collective dynamics.

Findings

Identification of first and second order phase transitions.

Discovery of the Rotational Splintered Phase Wave state.

Observation of cascade synchronization at a specific coupling value.

Abstract

Systems of oscillators whose internal phases and spatial dynamics are coupled, swarmalators, present diverse collective behaviors which in some cases lead to explosive synchronization in a finite population as a function of the coupling parameter between internal phases. Near the synchronization transition, the phase energy of the particles is represented by the XY model, and they undergo a transition which can be of the first order or second depending on the distribution of natural frequencies of their internal dynamics. The first order transition is obtained after an intermediate state (Static Wings Phase Wave state (SWPW)) from which the nodes, in cascade over time, achieve complete phase synchronization at a precise value of the coupling constant. For a particular case of natural frequencies distribution, a new phenomenon of Rotational Splintered Phase Wave state (RSpPW) is observed and leads progressively to synchronization through clusters switching alternatively from one to two and for which the frequency decreases as the phase coupling increases.