Battogtokh, D.Tyson, John J.2016-12-092016-12-092004-09-01Battogtokh, D.; Tyson, J. J., "bifurcation analysis of a model of the budding yeast cell cycle," Chaos 14, 653 (2004); http://dx.doi.org/10.1063/1.17800111054-1500http://hdl.handle.net/10919/73626We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces cerevisiae. We show that Clb2-dependent kinase exhibits bistability (stable steady states of high or low kinase activity). The transition from low to high Clb2-dependent kinase activity is driven by transient activation of Cln2-dependent kinase, and the reverse transition is driven by transient activation of the Clb2 degradation machinery. We show that a four-variable model retains the main features of the nine-variable model. In a three-variable model exhibiting birhythmicity (two stable oscillatory states), we explore possible effects of extrinsic fluctuations on cell cycle progression. (C) 2004 American Institute of Physics.653 - 661 (9) page(s)In CopyrightMathematics, AppliedPhysics, MathematicalMathematicsPhysicsMATHEMATICS, APPLIEDPHYSICS, MATHEMATICALMATHEMATICAL-MODELMOLECULAR-MODELFISSION YEASTDYNAMICSNOISEBIRHYTHMICITYOSCILLATIONSTRANSITIONSHYSTERESISCIRCUITSArticle - Refereedhttps://doi.org/10.1063/1.1780011143