On the basins of attraction of the regular autonomous asynchronous systems

TL;DR

This paper investigates the basins of attraction, fixed points, and limit sets of regular autonomous asynchronous Boolean systems, highlighting differences from synchronous systems and providing theoretical insights into their dynamical behavior.

Contribution

It offers a detailed study of the basins of attraction and limit sets in asynchronous Boolean systems, an area less explored compared to synchronous systems.

Findings

Characterization of basins of attraction for fixed points

Analysis of orbits and ω-limit sets in asynchronous systems

Differences between asynchronous and synchronous system behaviors

Abstract

The Boolean autonomous dynamical systems, also called regular autonomous asynchronous systems are systems whose 'vector field' is a function {\Phi}:{0,1}^{n}{\to}{0,1}^{n} and time is discrete or continuous. While the synchronous systems have their coordinate functions {\Phi}_{1},...,{\Phi}_{n} computed at the same time: {\Phi},{\Phi}{\circ}{\Phi},{\Phi}{\circ}{\Phi}{\circ}{\Phi},... the asynchronous systems have {\Phi}_{1},...,{\Phi}_{n} computed independently on each other. The purpose of the paper is that of studying the basins of attraction of the fixed points, of the orbits and of the {\omega}-limit sets of the regular autonomous asynchronous systems. The bibliography consists in analogies.