On the basins of attraction of the regular autonomous asynchronous systems

Abstract

The Boolean autonomous dynamical systems, also called regular autonomous asynchronous systems are systems whose 'vector field' is a function Φ:{0,1}^{n}{\to}{0,1}^{n} and time is discrete or continuous. While the synchronous systems have their coordinate functions Φ_{1},...,Φ_{n} computed at the same time: Φ,Φ{\circ}Φ,Φ{\circ}Φ{\circ}Φ,... the asynchronous systems have Φ_{1},...,Φ_{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 ω-limit sets of the regular autonomous asynchronous systems. The bibliography consists in analogies.

21 pages, Acta universitatis apulensis, Mathematics-informatics, special issue, 2011. arXiv admin note: substantial text overlap with arXiv:1012.5838