Dynamical bifurcation of multi-frequency oscillations in a fast-slow system

TL;DR

This paper investigates how slow parameter changes in a fast-slow system lead to bifurcations resulting in multi-frequency oscillations, highlighting transient dynamics towards invariant tori.

Contribution

It introduces a dynamical framework for understanding bifurcations to invariant tori in fast-slow systems with interconnected phase variables.

Findings

Transient damping oscillations evolve into multi-frequency oscillations.

Slow parameter evolution causes bifurcation to invariant tori.

The system exhibits asymptotic convergence to motions on the invariant torus.

Abstract

We study a dynamical counterpart of bifurcation to invariant torus for a system of interconnected fast phase variables and slowly varying parameters. We show that in such a system, due to the slow evolution of parameters, there arise transient processes from damping oscillations to multi-frequency ones, asymptotically close to motions on the invariant torus.