Gibbs Measures on Attractors in Biological Neural Networks

: We consider a class of nonreversible processes with a local interaction as a model of biological neural networks. We study the structure of equilibrium measures on attractors. There exist first and second order phase transitions with respect to the grey level parameter. Key-words: neural networks, attractor, phase transitions, grey level, cerebellar cortex. (R'esum'e : tsvp) Postal address: University of Lund, Department of Mathematical Statistics, Box 118, S-221 00 Lund, Sweden Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Telephone : (33) 01 39 63 55 11 -- Telecopie : (33) 01 39 63 53 Mesures de Gibbs sur les Attracteurs dans les R'eseaux de Neurones Biologiques. R'esum'e : On consid`ere des processus stochastiques non reversibles `a interaction locale comme un mod`ele de reseaux de neurones biologiques. Mots-cl'e : r'eseaux de neurones, transition de phase, attracteur. Gibbs Measures on Attractors in Biolo..