title: Dynamics of random Boolean networks under fully asynchronous stochastic update based on linear representation.
abstract: 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 length[Formula: see text] in 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.
authors.affiliation: Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China.
authors.forename: Chao
authors.initials: C
authors.lastname: Luo
authors.forename: Xingyuan
authors.initials: X
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D053263:Gene Regulatory Networks; D008954:Models, Biological; D008962:Models, Theoretical