  Applying the mathematical circulation theory of Markov chains, we investigate
the synchronized stochastic dynamics of a discrete network model of yeast
cell-cycle regulation where stochasticity has been kept rather than being
averaged out. By comparing the network dynamics of the stochastic model with
its corresponding deterministic network counterpart, we show that the
synchronized dynamics can be soundly characterized by a dominant circulation in
the stochastic model, which is the natural generalization of the deterministic
limit cycle in the deterministic system. Moreover, the period of the main peak
in the power spectrum, which is in common use to characterize the synchronized
dynamics, perfectly corresponds to the number of states in the main cycle with
dominant circulation. Such a large separation in the magnitude of the
circulations, between a dominant, main cycle and the rest, gives rise to the
stochastic synchronization phenomenon.
