The new explanation of cluster synchronization in the generalized Kuramoto system

TL;DR

This paper introduces a novel transformation based on the periodic properties of the density function to explain cluster synchronization in the generalized Kuramoto system, providing new insights into its sensitivity and boundary behavior.

Contribution

It presents a new symmetry transformation approach that explains cluster synchronization and its initial condition sensitivity in the generalized Kuramoto system.

Findings

The transformation reveals the periodic nature of the density function.

Cluster boundaries act like barriers, influencing synchronization sensitivity.

Numerical results confirm the theoretical predictions.

Abstract

The cluster synchronization is a very important characteristic for the higher harmonic coupling Kuramoto system. A novel transformation is provided, and it gives cluster synchronization by the periodic properties of the density function. The periodic properties of the density function also make the cluster sections' boundaries barrier-like, which helps to explain the sensitiveness of cluster synchronization on the initial conditions of the oscillators. Detailed numerical studies confirm the theoretical predictions from this new view of the symmetry transformation. The work is very beneficial to the further study on cluster synchronization in various systems.