2009/04/15 by Hao Ge, Hong Qian, Ge, Hao +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #FOS: Biological sciences #Gene Regulatory Network Analysis #Molecular Networks (q-bio.MN) #Nonlinear Dynamics and Pattern Formation #q-bio.MN #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.0904.2254
23 pages,6 figures; in Mathematical Bioscience 2008
arxiv created 2009/04/15 · openalex publication_date 2009/04/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
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.