The influence of noise on two- and three-frequency quasi-periodicity in a simple model system

TL;DR

This paper investigates how noise affects the dynamics of a simple 3D map exhibiting two- and three-frequency quasi-periodicity, analyzing bifurcation changes using Lyapunov charts.

Contribution

It introduces an analysis of noise effects on quasi-periodic systems using Lyapunov charts, focusing on bifurcation transformations in a minimal 3D map.

Findings

Noise alters the dynamical regimes of quasi-periodic systems.

Lyapunov exponents reveal bifurcation modifications due to noise.

The study characterizes the impact of noise on the birth of 3-tori.

Abstract

We discuss the effect of noise on a system with a quasi-periodicity of different dimensions. As the basic model of our research we use the simplest three-dimensional map with two-frequency and three-frequency quasi-periodicity. Modification of the dynamical regimes at the influence of noise is considered with the help of Lyapunov chart method. The transformation of Lyapunov exponents plots characteristic for the quasi-periodic Hopf bifurcation of 3-torus birth at the presence of noise is examined.