Abstract
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.
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