Numerical Coalescence of Chaotic Trajectories

TL;DR

This paper investigates how finite precision in numerical computations causes chaotic trajectories to coalesce, revealing frequent occurrences and linking the phenomenon to a universality class of chaotic systems through a first-passage process model.

Contribution

It introduces a model connecting numerical coalescence of chaotic trajectories to a first-passage process, applicable across various chaotic systems and particle aggregation scenarios.

Findings

Numerical coalescence occurs surprisingly frequently in chaotic systems.

The phenomenon can be modeled as a first-passage process.

Results are relevant for particle aggregation and numerical analysis of chaos.

Abstract

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to a universality class of chaotic systems where this numerical coincidence effect can be described by mapping it to a first-passage process. Our results are applicable to aggregation of small particles in random flows, as well as to numerical investigation of chaotic systems.