Document Type

Article

Publication Date

6-2007

Publication Title

Physica A: Statistical Mechanics and its Applications

Volume

379

Issue

1

First Page

334

Last Page

356

Abstract

In this paper, we explore both numerically and analytically the robustness of a synchronous Boolean network governed by rule 126 of cellular automata. In particular, we explore whether or not the introduction of noise into the system has any discernable effect on the evolution of the system. This noise is introduced by changing the states of a given number of nodes in the system according to certain rules. New mathematical models are developed for this purpose. We use MATLAB to run the numerical simulations including iterations of the real system and the model, computation of Lyapunov exponents, and generation of bifurcation diagrams. We provide a more in-depth fixed-point analysis through analytic computations paired with a focus on bifurcations and delay plots to identify the possible attractors. We show that it is possible either to attenuate or to suppress entirely chaos through the introduction of noise and that the perturbed system may exhibit very different long-term behavior than that of the unperturbed system.

Comments

This article was originally published here: http://www.sciencedirect.com/science/article/pii/S0378437107000283.

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

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