Cycles of periodically time-variant Boolean networks

This paper investigates cycles of periodically time-variant Boolean networks (PTVBNs). Some properties of cycles of PTVBNs and the relationship between PTVBNs and time-invariant Boolean networks (TIBNs) are revealed. It is shown that each cycle of a PTVBN corresponds to a common cycle of some TIBNs. And, all the cycles of a PTVBN can be constructed by those of the corresponding TIBNs. Moreover, some results on lengths of cycles of PTVBNs are derived. Finally, some examples are given to illustrate the obtained theoretical results.