title: Coexistence of Quantized, Time Dependent, Clusters in Globally Coupled Oscillators.
abstract: We report on a novel collective state, occurring in globally coupled nonidentical oscillators in the proximity of the point where the transition from the system's incoherent to coherent phase converts from explosive to continuous. In such a state, the oscillators form quantized clusters, where neither their phases nor their instantaneous frequencies are locked. The oscillators' instantaneous speeds are different within the clusters, but they form a characteristic cusped pattern and, more importantly, they behave periodically in time so that their average values are the same. Given its intrinsic specular nature with respect to the recently introduced Chimera states, the phase is termed the Bellerophon state. We provide an analytical and numerical description of Bellerophon states, and furnish practical hints on how to seek them in a variety of experimental and natural systems.
authors.affiliation: Department of Physics, East China Normal University, Shanghai 200241, China.
authors.forename: Hongjie
authors.initials: H
authors.lastname: Bi
authors.affiliation: Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China.
authors.forename: Xin
authors.initials: X
authors.lastname: Hu
authors.affiliation: CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.|The Embassy of Italy in Tel Aviv, 25 Hamered Street, 68125 Tel Aviv, Israel.
authors.forename: S
authors.initials: S
authors.lastname: Boccaletti
authors.affiliation: School of Physics and Information Technology, Shaanxi Normal University, Xian 710062, China.
authors.forename: Xingang
authors.initials: X
authors.lastname: Wang
authors.affiliation: Department of Physics, East China Normal University, Shanghai 200241, China.
authors.forename: Yong
authors.initials: Y
authors.lastname: Zou
authors.affiliation: Department of Physics, East China Normal University, Shanghai 200241, China.
authors.forename: Zonghua
authors.initials: Z
authors.lastname: Liu
authors.affiliation: Department of Physics, East China Normal University, Shanghai 200241, China.
authors.forename: Shuguang
authors.initials: S
authors.lastname: Guan