On cycles in functional graphs of circulant type gene networks with threshold functions

In this paper, the functioning of circulant type gene networks with threshold function are studied. All states of a system are classified according to the length of $0$-series and $1$-series. It is shown that all cycles of a functional graph are divided into two groups: cycles composed of states with long series and cycles composed of states with short series. Some lower estimate of the number of cycles in a functional graph is obtained. A construction for building cycles composed of states with short series is given.