Finite-time Lyapunov exponents of Strange Nonchaotic Attractors

TL;DR

This paper investigates the probability distributions of finite-time Lyapunov exponents in strange nonchaotic attractors, revealing how their statistical properties can differentiate various bifurcation routes in quasiperiodically forced systems.

Contribution

It provides a detailed analysis of the statistical properties of Lyapunov exponent distributions for SNAs created through different mechanisms, enhancing understanding of their dynamical characteristics.

Findings

Distributions vary with different bifurcation routes.

Variance and skewness distinguish SNA formation mechanisms.

Finite-time Lyapunov exponents characterize attractor types.

Abstract

The probability distribution of finite-time Lyapunov exponents provides an important characterization of dynamical attractors. We study such distributions for strange nonchaotic attractors (SNAs) created through several different mechanisms in quasiperiodically forced nonlinear dynamical systems. Statistical properties of the distributions such as the variance and the skewness also distinguish between SNAs formed by different bifurcation routes.