Anti-phase synchronization in a population of swarmalators

TL;DR

This paper investigates how different community interactions in swarmalators lead to various collective states, including synchronization, anti-phase, and chimera-like behaviors, supported by numerical and semi-analytical analyses.

Contribution

It introduces a model of community-divided swarmalators with varying interaction strengths and analyzes the emergence of diverse synchronization states.

Findings

Large inter-community phase coupling leads to static synchronization.

Small phase coupling results in anti-phase and chimera-like states.

Semi-analytical methods confirm the stability of these states.

Abstract

Swarmalators are oscillatory systems endowed with a spatial component, whose spatial and phase dynamics affect each other. Such systems can demonstrate fascinating collective dynamics resembling many real-world processes. Through this work, we study a population of swarmalators where they are divided into different communities. The strengths of spatial attraction, repulsion as well as phase interaction differ from one group to another. Also, they vary from inter-community to intra-community. We encounter, as a result of variation in the phase coupling strength, different routes to achieve the static synchronization state by choosing several parameter combinations. We observe that when the inter-community phase coupling strength is sufficiently large, swarmalators settle in the static synchronization state. On the other hand, with a significant small phase coupling strength the state of anti-phase synchronization as well as chimera-like coexistence of sync and async are realized. Apart from rigorous numerical results, we have been successful to provide semi-analytical treatment for the existence and stability of global static sync and the anti-phase sync states.