Local Graph Transformations Driven by Lyapunov Functionals
Éric Goles · Complex Systems · 1989
We study the dynamical behavior of automata networks defined by x(t + 1) = x(t) + f(Ax(t) + b); where A is a symmetric n x n matrix, b is a real n-vector and f is the subgradient of a con vex function . More precisely we prove, by using Lyapunov operators associated to the network, that the steady state behavior of these au tomata 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 unwrap ping (6). For this last application, we give bounds for the transient length.