Length of state cycles of random Boolean networks: an analytic study

In this paper we consider the mean length of transients and the length of s tate cycles in random Boolean networks. We present an approximate calculati on of these quantities as a function of the size and connectivity of the ne twork. where using an annealed approximation we derive a recursive formula for the length of steps of the system. Using the mean step length and an ef fective momentary' state space, we calculate an approximate formula for the probability distribution function (PDF) of the length of state cycles and transients. We compare this PDF with analytical results in special cases an d with simulations by the Monte Carlo procedure.