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The dynamic properties of the regulatory network governing the choice between lytic and lysogenic growths of coliphage lambda is studied using a Markov chain stochastic model. Our computer simulation confirms the finding by Li [Proc. Natl. Acad. Sci. USA 101, 4781 (2004)] on the dynamics of budding yeast: that the biological stationary states are global attractors; the biological pathways of lytic and lysogenic growths are attracting trajectories; and the network functions are robustly designed against structural perturbations. In addition, our model shows the stochastic switch from lysogen to lytic growth, which has been observed in experiments. A definition of pseudoenergy is introduced in the network dynamics to reveal a transitionlike behavior in the system.