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Plenary Lecture
Making Asynchronous Systems Theory by
Making Use of Dynamical Systems Theory
Dr. Serban E. Vlad
Oradea City Hall,
Piata Unirii, Nr. 1, 410100, Oradea,
ROMANIA
serban_e_vlad@yahoo.com
Abstract: An n-signal is a function x:R→{0,1}ⁿ that fulfills certain
inertia requirements and an autonomous asynchronous system is a non-empty
subset of the set of the n-signals. The autonomous asynchronous systems are
the (real time, binary spaces, no input and non- deterministic) models of
the autonomous asynchronous circuits from the digital electrical
engineering.
The naturalness of the import in the autonomous asynchronous systems theory
of some elementary notions from the dynamical systems theory: flows, orbits,
nullclins, fixed points, ω-limit points, recurrent points, periodicity,
invariant sets, dependence on the initial states, transitivity, attraction,
attractors, chaos, equivalence, static and dynamic bifurcation, symmetry- is
given by the existence of a generator function Φ:{0,1}ⁿ →{0,1}ⁿ (called
network function by Moisil) and of a vector field f: R ⁿ → R ⁿ that play the
same role in the two theories. The fundamental ideas of these theories
coincide to some extent and the tools of analysis are different, in the
sense that the asynchronous systems do not have linearizations, Jacobians,
multipliers, Poincare maps etc.
The purpose of the lecture is that of browsing in the context of the
autonomous asynchronous systems some usual concepts of the dynamical systems
theory.
Brief Biography of the Speaker:
Serban E. Vlad was born in 1959 and he works at present as
analyst-programmer at the Oradea City Hall. His professional interests
include asynchronous systems theory and binary valued mathematical analysis.
He is a member of ROMAI and of GAMM, the Romanian and the German societies
of applied and industrial mathematics. He is the author of the book
‘Asynchronous Systems Theory’ that was published by WSEAS in 2007.
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