Complex Systems

Exponential Transient Classes of Symmetric Neural Networks for Synchronous and Sequential Updating Download PDF

Eric Goles
Servet Martinez
Departamento de Ingeniería, Matemática,
Facultad de Ciencias Físicas y Matemáticas,
Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile


We exhibit a class of symmetric neural networks which synchronous iteration possesses an exponential transient length. In fact if is the set of nodes we prove the transient length satisfies . For sequential updating we get the bound . This behavior shows that the dynamics of these class of networks is complex while the steady states are simple: only fixed points or orbits of period 2.