Document Type

Article

Publication Date

8-2008

Publication Title

Physica A: Statistical Mechanics and its Applications

Volume

387

Issue

19-20

First Page

4947

Last Page

4958

Abstract

This study considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number of parent nodes. The network is analyzed when the connectivity k is fixed or variable. Making use of a Boolean rule that is a generalization of Rule 22 of elementary cellular automata, a generalized formula for providing the probability of finding a node in state 1 at a time t is determined. We show typical behaviors of the iterations, and we study the dynamics of the network through Lyapunov exponents, bifurcation diagrams, and fixed point analysis. We conclude that the network may exhibit stability or chaos depending on the underlying parameters. In general high connectivity is associated with a convergence to zero of the probability of finding a node in state 1 at time t. We also study analytically and numerically the dynamics of the network under a stochastic noise procedure. We show that under a smaller probability of disturbing the nodes through the noise procedure the system tends to exhibit more nodes in the same state. For many parameter combinations there is no critical value of the noise parameter below which the network remains organized and above which it behaves randomly.

Comments

This article was originally published here: http://www.sciencedirect.com/science/article/pii/S0378437108004044.

© 2008. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

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