Chimera states in spatiotemporal systems: Theory and Applications

In this paper, we propose a retrospective and summary on recent studies of chimera states. Chimera states demonstrate striking inhomogeneous spatiotemporal patterns emerging in homogeneous systems through unexpected spontaneous symmetry breaking, where the consequent spatiotemporal patterns are composed of both coherence and incoherence domains, respectively characterized by the synchronized and desynchronized motions of oscillators. Since the discovery of chimera states by Kuramoto and others, this striking collective behavior has attracted a great deal of research interest in the community of physics and related interdisciplinary fields from both theoretical and experimental viewpoints. In recent works exploring chimera states, rich phenomena such as the spiral wave chimera, multiple cluster chimera, amplitude chimera were observed from various types of model systems. Theoretical framework by means of self-consistency approach and Ott-Antonsen approach were proposed for further understanding to this symmetry-breaking-induced behavior. The stability and robustness of chimera states were also discussed. More importantly, experiments ranging from optical, chemical to mechanical designs successfully approve the existence of chimera states.