Modal synchronization of coupled bistable Van der Pol oscillators

TL;DR

This paper explores complex synchronization phenomena in coupled bistable Van der Pol oscillators, revealing new regimes and bifurcations through amplitude and phase analysis, including unexpected asymmetric synchronization behaviors.

Contribution

It introduces a simplified phase-based approach to analyze nonconventional synchronization regimes in coupled bistable oscillators, uncovering new bifurcation structures and nonstationary regimes.

Findings

Identification of amplitude synchronization with phase drift

Discovery of nonstationary asymmetric synchronization regimes

Revelation of rich bifurcation structures in the system

Abstract

The paper revisits recently revealed regimes of the "nonconventional synchronization" in systems of coupled bi-stable Van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges between the coupled oscillators. In the paper it is demonstrated that such responses correspond to synchronization of the modulation amplitudes between symmetric and antisymmetric modes of the system, with persistent phase drift. This observation substantially simplifies the treatment, reduces the dynamics to simple phase cylinder and allows to reveal a rich set of global and local bifurcations of limit cycles and tori in the system. Among other findings, one encounters an unexpected regime of nonstationary asymmetric synchronization.