Ge Hao, Qian Hong, Qian Min
School of Mathematical Sciences, Peking University, Beijing, PR China.
Math Biosci. 2008 Jan;211(1):132-52. doi: 10.1016/j.mbs.2007.10.003. Epub 2007 Oct 23.
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.
应用马尔可夫链的数学循环理论，我们研究了酵母细胞周期调控离散网络模型的同步随机动力学，其中随机性得以保留而非被平均掉。通过将随机模型的网络动力学与其相应的确定性网络对应物进行比较，我们表明同步动力学可以由随机模型中的主导循环合理地表征，这是确定性系统中确定性极限环的自然推广。此外，常用于表征同步动力学的功率谱主峰的周期，与具有主导循环的主周期中的状态数完美对应。主导主周期与其余周期在循环幅度上的如此大的差异，导致了随机同步现象。
