From template analysis to generating partitions II: Characterization of the symbolic encodings

TL;DR

This paper provides numerical evidence supporting an algorithm for constructing symbolic encodings of chaotic attractors, demonstrating its accuracy, consistency with other methods, and suitability for real-time applications.

Contribution

The paper introduces a validated algorithm for generating symbolic encodings of chaotic attractors that is accurate, efficient, and adaptable for real-time use.

Findings

Solutions are dynamically equivalent.

Partitions are highly generating and accurately estimate metric entropy.

The method naturally determines the optimal number of symbols.

Abstract

We give numerical evidence of the validity of a previously described algorithm for constructing symbolic encodings of chaotic attractors from a template analysis. We verify that the different solutions that can be found are dynamically equivalent, and that our approach yields results that are consistent with those obtained from methods based on homoclinic tangencies. This is further confirmed by verifying directly that the computed partitions are generating to a high degree of accuracy, and that they can be used to estimate precisely the metric entropy. It is also shown that the correct number of symbols needed to describe the dynamics is naturally provided, and that a compact parameterization of a partition can easily be determined, which makes our algorithm suitable for applications such as real-time encoding.