Swarmalators under competitive time-varying phase interactions

TL;DR

This paper investigates the complex collective behaviors of swarmalators with time-varying competitive phase interactions influenced by vision radius, revealing various asymptotic states and conditions for synchronization through numerical and analytical methods.

Contribution

It introduces a novel model of swarmalators with dynamic attractive and repulsive phase couplings based on sensing radius, analyzing emergent states and synchronization conditions.

Findings

Discovery of static cluster synchronization dependent on initial conditions.

Identification of static ring phase wave state and its radius.

Validation of theoretical results using Stuart-Landau oscillators.

Abstract

Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to the fascinating bidirectional interplay between phase and spatial dynamics. Although different coupling topologies have already been considered, here we introduce time-varying competitive phase interaction among swarmalators where the underlying connectivity for attractive and repulsive coupling varies depending on the vision (sensing) radius. Apart from investigating some fundamental properties like conservation of center of position and collision avoidance, we also scrutinize the cases of extreme limits of vision radius. The concurrence of attractive-repulsive competitive phase coupling allows the exploration of diverse asymptotic states, like static $\pi$, and mixed phase wave states, and we explore the feasible routes of those states through a detailed numerical analysis. In sole presence of attractive local coupling, we reveal the occurrence of static cluster synchronization where the number of clusters depends crucially on the initial distribution of positions and phases of each swarmalator. In addition, we analytically calculate the sufficient condition for the emergence of the static synchronization state. We further report the appearance of the static ring phase wave state and evaluate its radius theoretically. Finally, we validate our findings using Stuart-Landau oscillators to describe the phase dynamics of swarmalators subject to attractive local coupling.