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Biological functions in living cells are controlled by protein interaction and genetic networks. These molecular networks should be dynamically stable against various fluctuations which are inevitable in the living world. In this paper, we propose and study a stochastic model for the network regulating the cell cycle of the budding yeast. The stochasticity in the model is controlled by a temperature-like parameter β. Our simulation results show that both the biological stationary state and the biological pathway are stable for a wide range of “temperature”. There is, however, a sharp transition-like behavior at β_c, below which the dynamics are dominated by noise. We also define a pseudo energy landscape for the system in which the biological pathway can be seen as a deep valley.