Synchronization and Bellerophon states in conformist and contrarian oscillators.
The study of synchronization in generalized Kuramoto models has witnessed an intense boost in the last decade. Several collective states were discovered, such as partially synchronized, chimera, π or traveling wave states. We here consider two populations of globally coupled conformist and contrarian oscillators (with different, randomly distributed frequencies), and explore the effects of a frequency-dependent distribution of the couplings on the collective behaviour of the system. By means of linear stability analysis and mean-field theory, a series of exact solutions is extracted describing the critical points for synchronization, as well as all the emerging stationary coherent states. In particular, a novel non-stationary state, here named as Bellerophon state, is identified which is essentially different from all other coherent states previously reported in the Literature. A robust verification of the rigorous predictions is supported by extensive numerical simulations.
Department of Physics, East China Normal University, Shanghai, 200241, China.|Institute of Condensed Matter and Material Physics, School of Physics, Peking University, Beijing, 100871, China.
Tian
T
Qiu
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.
Stefano
S
Boccaletti
Department of Physics, Bar-Ilan University, 592000, Ramat Gan, Israel.
Ivan
I
Bonamassa
Department of Physics, East China Normal University, Shanghai, 200241, China.
Yong
Y
Zou
Department of Physics, East China Normal University, Shanghai, 200241, China.
Jie
J
Zhou
Department of Physics, East China Normal University, Shanghai, 200241, China.
Zonghua
Z
Liu
Department of Physics, East China Normal University, Shanghai, 200241, China.
Shuguang
S
Guan