Bistability and self-oscillations in cell cycle control. (English) Zbl 1093.92035

Summary: A qualitative model of cell cycle control is presented and its transition from bistability to limit cycle oscillations and vice versa is discussed. The origin of this model is the two-dimensional system of kinetic equations introduced by B. Novak et al. [Chaos 11, No. 1, 277–286 (2001; Zbl 0992.92022)] which is illustrated computationally and analytically. For this purpose a qualitative model is numerically reconstructed from the steady state behavior of the dynamical variables including the bifurcation parameter. Then, the reconstructed cubic polynomial model is generalized to an appropriate canonical form and is analyzed in terms of Lyapunov values. On this basis, the relationship between bistability and self-oscillatory behavior of mitotic cell cycle is approached qualitatively.


92C37 Cell biology
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D20 Stability of solutions to ordinary differential equations
93C95 Application models in control theory


Zbl 0992.92022
Full Text: DOI


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