TY  - JOUR
A1  - Vlasov, Vladimir
A1  - Rosenblum, Michael
A1  - Pikovskij, Arkadij
T1  - Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe-Strogatz integrability
JF  - Journal of physics : A, Mathematical and theoretical
N2  - As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations.
KW  - Kuramoto model
KW  - oscillator populations
KW  - integrability
KW  - perturbation theory
Y1  - 2016
U6  - https://doi.org/10.1088/1751-8113/49/31/31LT02
SN  - 1751-8113
SN  - 1751-8121
VL  - 49
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -