Dmitry Bolotov
Publications:
|
Bolotov D. I., Bolotov M. I., Smirnov L. A., Osipov G. V., Pikovsky A.
Twisted States in a System of Nonlinearly Coupled Phase Oscillators
2019, vol. 24, no. 6, pp. 717-724
Abstract
We study the dynamics of the ring of identical phase oscillators with nonlinear
nonlocal coupling. Using the Ott – Antonsen approach, the problem is formulated as a system
of partial derivative equations for the local complex order parameter. In this framework, we
investigate the existence and stability of twisted states. Both fully coherent and partially
coherent stable twisted states were found (the latter ones for the first time for identical
oscillators). We show that twisted states can be stable starting from a certain critical value
of the medium length, or on a length segment. The analytical results are confirmed with direct
numerical simulations in finite ensembles.
|