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Applying the mathematical circulation theory of Markov chains, we investigatethe synchronized stochastic dynamics of a discrete network model of yeastcell-cycle regulation where stochasticity has been kept rather than beingaveraged out. By comparing the network dynamics of the stochastic model withits corresponding deterministic network counterpart, we show that thesynchronized dynamics can be soundly characterized by a dominant circulation inthe stochastic model, which is the natural generalization of the deterministiclimit cycle in the deterministic system. Moreover, the period of the main peakin the power spectrum, which is in common use to characterize the synchronizeddynamics, perfectly corresponds to the number of states in the main cycle withdominant circulation. Such a large separation in the magnitude of thecirculations, between a dominant, main cycle and the rest, gives rise to thestochastic synchronization phenomenon.

Synchronized Dynamics and Nonequilibrium Steady States in a Stochastic Yeast Cell-Cycle Network