Synchronization measurement based on Poincaré’s sphere

Abstract Synchronization is an important phenomenon occurring in many complex systems, such as neural networks, power grids, or social networks. Various methods have been proposed to measure synchronization, each with its advantages and limitations. In this work, we introduce the Poincaré sphere a generalized of which provides useful tool visualize similarities between oscillations. We propose notion “total synchronization,” considers amplitude, frequency, phase all can be measured visualized simultaneously on sphere. show that visualizing oscillatory trajectories has over more typical two-dimensional representation, particularly cases where projection onto space cannot capture different Furthermore, apply new synchronization measurement linear nonlinear oscillators provide two concrete examples application jitter noisy oscillations quantizing solutions oscillator-based Ising machines. Our work demonstrates usefulness perspective studying systems.