Complex Systems

Local Graph Transformations Driven by Lyapunov Functionals Download PDF

Eric Goles
Departamento de Matemáticas, Escuela de Ingeniería,
Universidad de Chile, Casilla 170-Correo 3, Santiago, Chile


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.