Noise in random Boolean networks

Abstract

We investigate the effect of noise on Random Boolean Networks. Noise is implemented as a probability $p$ that a node does not obey its deterministic update rule. We define two order parameters, the long-time average of the Hamming distance between a network with and without noise, and the average frozenness, which is a measure of the extent to which a node prefers one of the two Boolean states. We evaluate both order parameters as function of the noise strength, finding a smooth transition from deterministic ($p=0$) to fully stochastic ($p=1/2$) dynamics for networks with $K\le 2$, and a first order transition at $p=0$ for $K>2$. Most of the results obtained by computer simulation are also derived analytically. The average Hamming distance can be evaluated using the annealed approximation. In order to obtain the distribution of frozenness as function of the noise strength, more sophisticated self-consistent calculations had to be performed. This distribution is a collection of delta peaks for K=1, and it has a fractal sructure for $K>1$, approaching a continuous distribution in the limit $K\gg 1$.

9 pages, 8 figures, 1 table

References in corpus (13)

• Genetic networks with canalyzing Boolean rules are always stable
• Number and length of attractors in a critical Kauffman model with connectivity one
• Ferromagnetic Phase Transition in Barabasi-Albert Networks
• Stable and unstable attractors in Boolean networks
• The dynamics of critical Kauffman networks under asynchronous stochastic update
• Canalizing Kauffman networks: non-ergodicity and its effect on their critical behavior
• On the number of attractors in random Boolean networks
• Special Attention Network
• The phase diagram of random threshold networks
• Numerical and Theoretical Studies of Noise Effects in the Kauffman Model
• On the properties of cycles of simple Boolean networks
• Multilayer neural networks with extensively many hidden units
• Response of Boolean networks to perturbations

Cited by in corpus (8)

• Emergence of robustness against noise: A structural phase transition in evolved models of gene regulatory networks
• Redundancy and error resilience in Boolean Networks
• Boolean networks with robust and reliable trajectories
• Dynamics of Boolean networks - an exact solution
• The behavior of noise-resilient Boolean networks with diverse topologies
• Phase transitions and memory effects in the dynamics of Boolean networks
• Interplay between degree and Boolean rules in the stability of Boolean networks
• Dynamics of attractor transitions in Boolean networks under noise