Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2011-08-22
J. Stat. Mech. (2012) P01006
Physics
Condensed Matter
Disordered Systems and Neural Networks
17 pages, 7 figures
Scientific paper
10.1088/1742-5468/2012/01/P01006
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the dynamics always undergoes a phase transition from a non-ergodic regime, where a memory of its past states is preserved, to an ergodic regime, where no such memory exists and every microstate is equally probable. Both the average error on the network, as well as the critical value of noise where the transition occurs are investigated analytically, and compared to numerical simulations. The results for "partially dense" networks, comprised of relatively few, but dynamically important nodes, which have a number of inputs which greatly exceeds the average for the entire network, give very general upper bounds on the maximum resilience against noise attainable on globally sparse systems.
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