Local Graph Transformations Driven by Lyapunov Functionals
Eric Goles
Departamento de Matemáticas, Escuela de Ingeniería,
Universidad de Chile, Casilla 170-Correo 3, Santiago, Chile
Abstract
We study the dynamical behavior of automata networks defined by 
; where 
is a symmetric 
matrix, 
is a real 
-vector and 
is the subgradient of a convex function. More precisely, that the steady state behavior of these automata is simple: fixed points or two-cycles. We also give bounds for the transient time needed to reach the steady state. These networks appear in applications such as image restauration or phase unwrapping [6]. For this last application, we give bounds for the transient length.
