Comparison of Topological Structures Between Boolean Control Networks and Nominal Boolean Networks

In this paper, comparison of topological structures between Boolean control networks and nominal Boolean networks is investigated. First, transient periods and attractor basins of Boolean control networks are introduced, and three necessary and sufficient conditions are derived in order to determine transient periods and attractor basins. From two aspects of attractors and transient periods, topological structures of Boolean control networks and nominal Boolean networks are compared, and the existences of different relations are illustrated via some examples. Finally, four necessary and sufficient conditions are proposed for judging relations of topological structures between Boolean control networks and nominal Boolean networks.