Structural Oscillatority Analysis of Boolean Networks

Boolean networks are system models whose binary-state nodes are interconnected. Although a number of studies have been conducted so far, it is usually assumed that the full information on the target system is available for analysis and design. This paper addresses a structural analysis problem for Boolean networks, i.e., the case when the information on the network structure is available but that on the node dynamics is unavailable. In particular, we consider here oscillatority (instability). First, the notion of structural oscillatority is formulated based on an equivalence relation of network structures. We next present a necessary and sufficient condition for the so-called cactus Boolean networks to be structurally oscillatory. This condition captures structural oscillatority by a simple characterization in terms of the network structure (more concretely, the number of inhibiting edges in each simple cycles), which enables us to apply it to large-scale Boolean networks.