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 state cycles in random Boolean networks. We present an approximate calculation of these quantities as a function of the size and connectivity of the network, 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 `effective 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 and with simulations by the Monte Carlo procedure.

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