Partially coherent twisted states in arrays of coupled phase oscillators

Abstract

We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorenztian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly twisted in space. To analyze these we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the wellknown Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system.