On a family of models of cell division cycle. (English) Zbl 1079.92028
Summary: The aim of this work is to generalize and study a model of cell division cycles proposed recently by Z. Zheng et al. [ibid. 11, 2371–2378 (2000; Zbl 0971.92013)]. We study the qualitative properties of a general family to which the above model belongs. The global asymptotic stability (GAS) of the unique equilibrium point \(E\) (idest of the arrest of cell cycling) is investigated and some conditions are given. Hopf bifurcations are shown to happen. In the second part of the work, the theorems given in the first part are used to analyze the GAS of \(E\) and improved conditions are given. The theorem on the uniqueness of limit cycles in Lienard systems is used to show that, for some combination of parameters, the model has GAS limit cycles.
MSC:
| 92C37 | Cell biology |
| 37N25 | Dynamical systems in biology |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
Citations:
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