Singular Perturbation of Nonlinear Dynamics by Parasitic Noise

TL;DR

This paper reveals that tiny parasitic higher-order dynamics caused by computer roundoff can lead to exponential divergence in nonlinear systems, fundamentally altering attractors and stability.

Contribution

It demonstrates for the first time that machine epsilon level parasitic noise can induce singular perturbations causing divergence in nonlinear dynamics.

Findings

Parasitic higher-order dynamics can cause divergence of attractors.

Divergence occurs exponentially regardless of chaos.

Singular perturbation by parasitic noise is a novel property.

Abstract

In nonlinear systems analysis, minor fractions of higher-order dynamics are often neglected for simplicity. Here, we show that machine epsilon levels of parasitic higher-order dynamics due to computer roundoff alone can cause divergence of the H\'enon attractor to new attractors or instability. The divergence develops exponentially regardless of whether the original or new attractor is chaotic or not. Such singular perturbation by parasitic higher-order dynamics is a novel property of nonlinear dynamics that is of wide practical significance in dynamical systems modeling, simulation and control.