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0022-4715/02/0800-0527/0 2002 Plenum Publishing Corporation Journal of Statistical Physics, Vol. 108, Nos. 3/4, August 2002 ( 2002)
 

Summary: 527
0022-4715/02/0800-0527/0 © 2002 Plenum Publishing Corporation
Journal of Statistical Physics, Vol. 108, Nos. 3/4, August 2002 (© 2002)
Dynamical Phase Transition in a Neural Network
Model with Noise: An Exact Solution
Cristián Huepe1
and Maximino Aldana-González1, 2
1
James Franck Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois
60637.
2
To whom correspondence should be addressed; e-mail: maximino@control.uchicago.edu
Received January 11, 2002; accepted March, 2002
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 gc of the noise, below which the network remains organized and
above which it behaves randomly. The existence and nature of the phase transi-
tion are computed analytically, showing that the critical exponent is 1/2. The

  

Source: Aldana, Maximino - Centro de Ciencias Físicas, Universidad Nacional Autónoma de México

 

Collections: Physics