Complex Systems

Vector Fields and Neural Networks Download PDF

R. Vilela Mendes
Theoretical Division, CERN, CH-1211, Geneva 23, Switzerland
Centro de Fisica da Materia Condensada, Av. Gama Pinto,
2-1699 Lisboa Codex, Portugal

J. Taborda Duarte
Laboratorio Nacional de Engenharia e Tecnologia Industrial,
Az. dos Lameiros, Estr. do Pacco do Lumiar, 1600 Lisboa, Portugal


We consider neural network models described by systems of (continuous time) differential equations. The dynamical nature of each model is identified, symmetric networks being related to gradient vector fields and asymmetric networks decomposed into their gradient and Hamiltonian components. From this identification follows, in particular, a simple characterization of structural stability for symmetric networks and a limit cycle analysis of asymmetric networks as generators of coherent temporal patterns.