Characterize interactions among multiple solitary nodes and frequency clusters

Develop a detailed theory for the interaction of multiple solitary nodes with distinct mean frequencies, including configurations forming frequency clusters, in the inertial Kuramoto model on complex networks, and characterize their collective dynamics and stability properties.

Background

The paper focuses on 1-solitary states (a single solitary oscillator) and outlines in the supplement that the considerations extend to multiple solitary nodes. However, a comprehensive analysis of how multiple solitary nodes interact—potentially through shared resonant modes and mutual power flows—is not provided.

Understanding multi-solitary and frequency-cluster interactions is important in highly multistable regimes where several solitary states may coexist, influencing transient behavior, basin structure, and the response to localized perturbations.