Dynamical Phase Transition in a Neural Network Model with Noise: an Exact Solution
Abstract
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same value. It is shown that, under very general conditions, there exists a critical value of the noise, below which the network remains organized and above which it behaves randomly. The existence and nature of the phase transition are computed analytically, showing that the critical exponent is 1/2. The dependence of the critical noise on the parameters of the network is obtained. These results are then compared with two numerical realizations of the network.
 Publication:

arXiv eprints
 Pub Date:
 February 2002
 arXiv:
 arXiv:condmat/0202411
 Bibcode:
 2002cond.mat..2411H
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 17 pages, 6 figures, Submitted to the Jounal of Statistical Physics