Frustration Induced Chimeras and Motion in Two Dimensional Swarmalators

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.