Characterizing nonstationary coherent states in globally coupled conformist and contrarian oscillators

Tian Qiu; S Boccaletti; Zonghua Liu; Shuguang Guan

doi:10.1103/PhysRevE.100.052310

Characterizing nonstationary coherent states in globally coupled conformist and contrarian oscillators

Phys Rev E. 2019 Nov;100(5-1):052310. doi: 10.1103/PhysRevE.100.052310.

Authors

Tian Qiu^{1

2}, S Boccaletti^{3

4}, Zonghua Liu¹, Shuguang Guan¹

Affiliations

¹ Department of Physics, East China Normal University, Shanghai 200241, China.
² Institute of Condensed Matter and Material Physics, School of Physics, Peking University, Beijing 100871, China.
³ CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.
⁴ Unmanned Systems Research Institute, Northwestern Polytechnical University, Xi'an 710072, China.

PMID: 31870024
DOI: 10.1103/PhysRevE.100.052310

Abstract

For decades, the description and characterization of nonstationary coherent states in coupled oscillators have not been available. We here consider the Kuramoto model consisting of conformist and contrarian oscillators. In the model, contrarians are chosen from a bimodal Lorentzian frequency distribution and flipped into conformists at random. A complete and systematic analytical treatment of the model is provided based on the Ott-Antonsen ansatz. In particular, we predict and analyze not only the stability of all stationary states (such as the incoherent, the π, and the traveling-wave states), but also that of the two nonstationary states: the Bellerophon and the oscillating-π state. The theoretical predictions are fully supported by extensive numerical simulations.