Universal Regular Autonomous Asynchronous Systems: Fixed Points, Equivalencies and Dynamic Bifurcations

TL;DR

This paper investigates the fundamental properties of universal regular autonomous asynchronous systems, focusing on fixed points, equivalencies, and bifurcations, using analogies with dynamical systems theory to deepen understanding.

Contribution

It defines and characterizes fixed points, equivalencies, and bifurcations in universal regular autonomous asynchronous systems, extending the theoretical framework with dynamical systems analogies.

Findings

Identification of fixed points in asynchronous systems

Characterization of system equivalencies

Analysis of dynamical bifurcations

Abstract

The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In the autonomous version, such a system is a set of functions x:R{\to}{0,1}^{n} called states (R is the time set). If an asynchronous system is defined by making use of a so called generator function {\Phi}:{0,1}^{n}{\to}{0,1}^{n}, then it is called regular. The property of universality means the greatest in the sense of the inclusion. The purpose of the paper is that of defining and of characterizing the fixed points, the equivalencies and the dynamical bifurcations of the universal regular autonomous asynchronous systems. We use analogies with the dynamical systems theory.