Oscillations and synchronization in a system of three reactively coupled oscillators

TL;DR

This paper analyzes the dynamics of three reactively coupled van der Pol oscillators, deriving phase equations and exploring bifurcations and synchronization phenomena through Lyapunov exponent charts.

Contribution

It introduces a systematic derivation of phase equations for a three-oscillator system with reactive coupling and analyzes their bifurcation structure.

Findings

Reactive coupling influences synchronization patterns

Bifurcation analysis reveals complex dynamical regimes

Lyapunov charts illustrate stability regions

Abstract

We consider a system of three interacting van der Pol oscillators with reactive coupling. Phase equations are derived, using proper order of expansion over the coupling parameter. The dynamics of the system is studied by means of the bifurcation analysis and with the method of Lyapunov exponent charts. Essential and physically meaningful features of the reactive coupling are discussed.