Following the complete sequencing of several genomes, interest has grown in the construction of genetic regulatory networks, which attempt to describe how different genes work together in both normal and abnormal cells. This interest has led to significant research in the behavior of abstract network models, with Boolean networks emerging as one particularly popular type. An important limitation of these networks is that their time evolution is necessarily periodic, motivating our interest in alternatives that are capable of a wider range of dynamic behavior. In this paper we examine one such class, that of continuous-time Boolean networks, a special case of the class of Boolean delay equations (BDEs) proposed for climatic and seismological modeling. In particular, we incorporate a biologically motivated refractory period into the dynamic behavior of these networks, which exhibit binary values like traditional Boolean networks, but which, unlike Boolean networks, evolve in continuous time. In this way, we are able to overcome both computational and theoretical limitations of the general class of BDEs while still achieving dynamics that are either aperiodic or effectively so, with periods many orders of magnitude longer than those of even large discrete time Boolean networks.
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