Synchronization of coupled stick-slip oscillators

TL;DR

This paper investigates how coupled stick-slip oscillators synchronize, revealing different phase behaviors depending on coupling strength and oscillator similarity, using phase reduction analysis.

Contribution

It provides a systematic analysis of synchronization phenomena in coupled stick-slip oscillators, including multi-oscillator configurations, using phase reduction methods.

Findings

Identifies anti-phase synchronization in identical oscillator pairs.

Shows in-phase tendency in non-identical pairs with weak coupling.

Demonstrates partial synchronization in three-oscillator systems.

Abstract

A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical Hopf bifurcation. The two-oscillator system that has similar weakly coupled oscillators exhibits synchronization in a parameter range. The synchronization has an anti-phase nature for an identical pair. However, it tends to be more in-phase for a non-identical pair with a rather weak coupling. A system of three identical oscillators (1, 2, and 3) coupled in a line (with two springs k12=k23) exhibits synchronization with two of them (1 and 2 or 2 and 3) being nearly in-phase. These collective behaviours are systematically estimated using the phase reduction method.