Pattern selection in a ring of Kuramoto oscillators

TL;DR

This paper investigates the complex synchronization patterns in a ring of Kuramoto oscillators, revealing new unstable states and highlighting the limitations of predicting final states due to saddle points.

Contribution

It introduces novel unstable states in Kuramoto rings and compares methods for predicting the system's final stationary state.

Findings

Discovery of new unstable states in the system

Limitations in predicting final states due to saddle points

Comparison of different forecasting methods

Abstract

Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity of the dynamics in the high dimensional state-space of this system. Beside the known stable stationary points novel unstable states are revealed. We find that the prediction of the final stationary state is limited by the presence of such saddle points. This is illustrated by considering and comparing two different attempts for forecasting the final stationary state