title: Intrinsic properties of Boolean dynamics in complex networks.
abstract: We study intrinsic properties of attractor in Boolean dynamics of complex networks with scale-free topology, comparing with those of the so-called Kauffman's random Boolean networks. We numerically study both frozen and relevant nodes in each attractor in the dynamics of relatively small networks (20<or=N<or=200). We investigate numerically robustness of an attractor to a perturbation. An attractor with cycle length of l(c) in a network of size N consists of l(c) states in the state space of 2(N) states; each attractor has the arrangement of N nodes, where the cycle of attractor sweeps l(c) states. We define a perturbation as a flip of the state on a single node in the attractor state at a given time step. We show that the rate between unfrozen and relevant nodes in the dynamics of a complex network with scale-free topology is larger than that in Kauffman's random Boolean network model. Furthermore, we find that in a complex scale-free network with fluctuation of the in-degree number, attractors are more sensitive to a state flip for a highly connected node (i.e. input-hub node) than to that for a less connected node. By some numerical examples, we show that the number of relevant nodes increases, when an input-hub node is coincident with and/or connected with an output-hub node (i.e. a node with large output-degree) one another.
authors.affiliation: Graduate School of Science and Technology, Niigata University, Nishi-ku Ikarashi 2-Nochou 8050, Niigata 950-2181, Japan. f01j006g@mail.cc.niigata-u.ac.jp
authors.forename: Shu-ichi
authors.initials: S
authors.lastname: Kinoshita
authors.forename: Kazumoto
authors.initials: K
authors.lastname: Iguchi
authors.forename: Hiroaki S
authors.initials: HS
authors.lastname: Yamada
mesh_terms: D000818:Animals; D003198:Computer Simulation; D005786:Gene Expression Regulation; D053263:Gene Regulatory Networks; D006801:Humans; D008957:Models, Genetic; D017711:Nonlinear Dynamics