On a family of models of cell division cycle

Alberto D'Onofrio

Research output: Contribution to journalArticle


The aim of this work is to generalize and study a model of cell division cycle proposed recently by Zheng et al. [Zheng Z, Zhou T, Zhang S. Dynamical behavior in the modeling of cell division cycle. Chaos, Solitons & Fractals 2000;11:2371-8]. Here 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's bifurcation is showed 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. Theorem on uniqueness of limit cycle in Lienard's systems are used to show that, for some combination of parameters, the model has GAS limit cycles.

Original languageEnglish
Pages (from-to)1205-1212
Number of pages8
JournalChaos, Solitons and Fractals
Issue number5
Publication statusPublished - Mar 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics

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