Document Type

Article

Publication Date

5-2004

Publication Title

Physical Review E

Volume

69

Abstract

This paper considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number of parent nodes, which may vary from one node to another. This is an extension of a model studied by Andrecut and Ali ( [5]) who consider the same number of parents for all nodes. We make use of the same Boolean rule as the authors of [5], provide a generalization of the formula for the probability of finding a node in state 1 at a time t and use simulation methods to generate consecutive states of the network for both the real system and the model. The results match well. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the route to chaos is due to a cascade of period-doubling bifurcations which turn into reversed (period - halving) bifurcations for certain combinations of parameter values.

Comments

This article was originally published here: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.69.056214.

Download

Included in

Mathematics Commons

Share

COinS