Solvable dynamics in a system of interacting random tops

TL;DR

This paper introduces a new exactly solvable model of synchronization involving interacting tops with random precession frequencies, enabling detailed analysis of orientational effects and stability in synchronized states.

Contribution

The paper presents a novel solvable model of synchronization dynamics with long-range interactions and orientational disorder, expanding understanding of collective behavior in such systems.

Findings

Incoherent state stability depends on disorder type.

Systems with only orientational disorder synchronize without external noise.

Explicit stability analysis of synchronized and incoherent states.

Abstract

In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in synchronized phenomena. A stability analysis of the incoherent solution is performed for different types of orientational disorder. A system with only orientational disorder always synchronizes in the absence of external noise.