Reachability and synchronization of hierarchical Boolean control networks

This paper investigates the reachability and synchronization problems for hierarchial Boolean control networks (BCNs). Here, we assume that the nodes are only affected by the nodes in the same layer network and the nodes from the previous layer network, meanwhile only affect the nodes from the next layer network. Firstly, the reachability is investigated and two notions of reachability are presented, i.e. group-reachability and simultaneous-reachability. Then, some necessary and sufficient criteria are obtained to guarantee group-reachability and simultaneous-reachability respectively. Secondly, based on the algebraic representation of the studied model, synchronization is analytically discussed respectively under free control sequences. Finally, numerical example is presented to show the validness of our main results.