Frustration Induced Chimeras and Motion in Two Dimensional Swarmalators

TL;DR

This paper investigates how a frustration parameter influences the emergence of complex, non-stationary, and chimeric collective states in a two-dimensional swarmalator model, revealing new dynamical behaviors driven by phase interaction frustration.

Contribution

It introduces a two-dimensional swarmalator model with a frustration parameter, demonstrating its role in generating novel non-stationary and chimeric states not seen in previous models.

Findings

Frustration induces non-stationary, chimeric, and translational states.

Phase non-stationarity affects spatial arrangements of swarmalators.

Classification of states based on order parameters.

Abstract

Swarmalators are phase oscillators capable of simultaneous swarming and synchronization, making them potential candidates for replicating complex dynamical states. In this work, we explore the effects of a frustration parameter in the phase interaction functions of a two-dimensional swarmalator model inspired by the solvable Sakaguchi-swarmalators that move in a one-dimensional ring. The impact of the frustration parameter in these models has been a topic of great interest. Real-world coupled systems with frustration exhibit remarkable collective dynamical states, underscoring the relevance of this study. The frustration parameter induces various states exhibiting non-stationarity, chimeric clustering, and global translational motion, where swarmalators move spontaneously in two-dimensional space. We investigate the characteristics of these states and their responses to changes in the frustration parameter. Notably, the emergence of chimeric states suggests the crucial role of non-stationarity in phase interactions for spontaneous population clustering. Additionally, we examine how phase non-stationarity influences the spatial positions of swarmalators and provide a classification of these states based on different order parameters.