Synchronization of forced quasi-periodic coupled oscillators

TL;DR

This paper investigates how external forces synchronize coupled self-oscillators, mapping out different dynamic regimes and their characteristics using Lyapunov exponents and visual charts.

Contribution

It provides a detailed analysis of synchronization regimes and introduces visualization techniques for resonant tori in forced quasi-periodic oscillators.

Findings

Identified domains of complete and partial synchronization.

Mapped regimes of two- and three-frequency quasi-periodic oscillations.

Revealed differences between mode locking and beats in oscillator regimes.

Abstract

The problem of synchronization of coupled self-oscillators by external force is studied. The charts of Lyapunov's exponents in the "frequency - amplitude" parameter plane are obtained within the framework of the phase approximation. We identified the characteristic configurations of the domains of complete synchronization, two- and three-frequency quasi-periodic oscillations and different variants of partial synchronization of oscillators by an external force. The differences between regimes of mode locking and beats of partial oscillators are revealed and discussed. To visualize and analyze the domains of resonant two-frequency tori we construct the charts, in which regions of dynamics with different winding numbers are represented by colors.