TY - JOUR

T1 - The behavior of noise-resilient Boolean networks with diverse topologies

AU - Peixoto, Tiago P.

PY - 2012/1/10

Y1 - 2012/1/10

N2 - 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 and the critical value of noise where the transition occurs are investigated analytically, and compared to numerical simulations. The results for 'partially dense' networks, comprising relatively few, but dynamically important nodes, which have a number of inputs that greatly exceeds the average for the entire network, give very general upper bounds on the maximum resilience against noise attainable on globally sparse systems.

AB - 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 and the critical value of noise where the transition occurs are investigated analytically, and compared to numerical simulations. The results for 'partially dense' networks, comprising relatively few, but dynamically important nodes, which have a number of inputs that greatly exceeds the average for the entire network, give very general upper bounds on the maximum resilience against noise attainable on globally sparse systems.

UR - http://dx.doi.org/10.1088/1742-5468/2012/01/P01006

U2 - 10.1088/1742-5468/2012/01/P01006

DO - 10.1088/1742-5468/2012/01/P01006

M3 - Article

VL - 2012

JO - Journal of Statistical Mechanics-Theory and Experiment

JF - Journal of Statistical Mechanics-Theory and Experiment

SN - 1742-5468

M1 - P01006

ER -