2017/05/02 by Zuguang Gao, Xudong Chen, Gao, Zuguang +3
Biochemistry, Genetics and Molecular Biology · #Bacterial Genetics and Biotechnology #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Optimization and Control (math.OC) #Receptor Mechanisms and Signaling
paper · pdf · doi:10.48550/arxiv.1705.00759
openalex publication_date 2017/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Boolean network is a finite state discrete time dynamical system. At each step, each variable takes a value from a binary set. The value update rule for each variable is a local function which depends only on a selected subset of variables. Boolean networks have been used in modeling gene regulatory networks. We focus in this paper on a special class of Boolean networks, namely the conjunctive Boolean networks (CBNs), whose value update rule is comprised of only logic AND operations. It is known that any trajectory of a Boolean network will enter a periodic orbit. Periodic orbits of a CBN have been completely understood. In this paper, we investigate the orbit-controllability and state-controllability of a CBN: We ask the question of how one can steer a CBN to enter any periodic orbit or to reach any final state, from any initial state. We establish necessary and sufficient conditions for a CBN to be orbit-controllable and state-controllable. Furthermore, explicit control laws are presented along the analysis.