2017/08/07 by Xudong Chen, Chen, Xudong, Zuguang Gao +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · #Bioinformatics and Genomic Networks #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.1708.01975
openalex publication_date 2017/08/07 · openalex created_date 2017/08/17 · openalex updated_date 2026/07/28
A conjunctive Boolean network (CBN) is a finite state dynamical system, whose variables take values from a binary set, and the value update rule for each variable is a Boolean function consisting only of logic AND operations. We investigate the asymptotic behavior of CBNs by computing their periodic orbits. When the underlying digraph is strongly connected, the periodic orbits of the associated CBN has been completely understood, one-to-one corresponding to binary necklaces of a certain length given by the loop number of the graph. We characterize in the paper the periodic orbits of CBNs over an arbitrary weakly connected digraphs. We establish, among other things, a new method to investigate their asymptotic behavior. Specifically, we introduce a graphical-approach, termed system reduction, which turns the underlying digraph into a special weakly connected digraph whose strongly connected components are all cycles. We show that the reduced system uniquely determines the asymptotic behavior of the original system. Moreover, we provide a constructive method for computing the periodic orbit of the reduced system, which the system will enter for a given but arbitrary initial condition.