Open AccessDynamics of Random Boolean Networks under Fully Asynchronous Stochastic Update Based on Linear Representation
Author(s) -
Chao Luo,
Xingyuan Wang
Publication year - 2013
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0066491
Subject(s) - asynchronous communication , attractor , boolean network , representation (politics) , algebraic number , computer science , mathematics , theoretical computer science , discrete mathematics , boolean function , algorithm , mathematical analysis , computer network , politics , political science , law
A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of lengthin ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.