Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
In this paper we study the transition to synchrony in an
one-dimensional array of oscillators with non-local coupling. For its
description in the continuum limit of a large number of phase oscillators, we
use a corresponding Ott-Antonsen equation, which is an integrodifferential
equation for the evolution of the macroscopic profiles of the local mean
field. Recently, it has been reported that in the spatially extended case at
the synchronization threshold there appear partially coherent plane waves
with different wave numbers, which are organized in the well-known Eckhaus
scenario. In this paper, we show that for Kuramoto-Sakaguchi phase
oscillators the phase lag parameter in the interaction function can induce a
Benjamin-Feir type instability of the partially coherent plane waves. The
emerging collective macroscopic chaos appears as an intermediate stage
between complete incoherence and stable partially coherent plane waves.We
give an analytic treatment of the Benjamin-Feir instability and its onset in
a codimension-two bifurcation in the Ott-Antonsen equation as well as a
numerical study of the transition from phase turbulence to amplitude
turbulence inside the Benjamin-Feir unstable region