2002/02/22 by Cristián Huepe, Cristian Huepe, Huepe, Cristian +2
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.cond-mat/0202411
17 pages, 6 figures, Submitted to the Jounal of Statistical Physics
arxiv created 2002/02/22 · openalex publication_date 2002/02/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.