Cycles of functioning of regulatory circuits of the gene network discrete models

The paper describes a new class of cycles of the functional graphs identified by the discrete models of the gene network regulatory circuits with the threshold functions. A description of the class of cycles is obtained depending on the value of $p$ which is the threshold weight of the functions values and the number of the network vertices $n$. $P$-property criterion is proved as well as the theorem of reducibility of the cycles description for any $p>3$ to the description of 4-property cycles and hereditary cycles for $p=3$. Ill. 1, bibliogr. 9.