Synchronization and Bellerophon states in conformist and contrarian oscillators

Tian Qiu, Stefano Boccaletti, Ivan Bonamassa, Yong Zou, Jie Zhou, Zonghua Liu, Shuguang Guan

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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.

Original languageEnglish
Article number36713
JournalScientific Reports
StatePublished - 9 Nov 2016

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© The Author(s) 2016.


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