Structured scale-dependence in the Lyapunov exponent of a Boolean chaotic map

TL;DR

This paper investigates how discontinuities in a Boolean chaotic map cause structured, scale-dependent variations in the Lyapunov exponent, revealing the impact of discrete logic elements on chaos dynamics.

Contribution

It introduces an experimental Boolean network model demonstrating how logic gate discontinuities influence the Lyapunov exponent's structure.

Findings

Discontinuities lead to structured scale dependence in Lyapunov exponents.

Boolean network chaos exhibits unique Lyapunov features due to logic gate effects.

A simple model explains the origin of these structured variations.

Abstract

We report on structures in a scale-dependent Lyapunov exponent of an experimental chaotic map that arise due to discontinuities in the map. The chaos is realized in an autonomous Boolean network which is constructed using asynchronous logic gates to form a map operator that outputs an unclocked pulse-train of varying widths. The map operator executes pulse-width stretching and folding and the operator's output is fed back to its input to continuously iterate the map. Using a simple model, we show that the structured scale-dependence in the system's Lyapunov exponent is the result of the discrete logic elements in the map operator's stretching function.