International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 51848, 15 pages

Linear and structural stability of a cell division process model

Vladimir Balan and Ileana Rodica Nicola

Department of Mathematics I, University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania

Received 11 June 2005; Revised 3 August 2005; Accepted 29 December 2005

Copyright © 2006 Vladimir Balan and Ileana Rodica Nicola. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper investigates the linear stability of mammalian physiology time-delayed flow for three distinct cases (normal cell cycle, a neoplasmic cell cycle, and multiple cell arrest states), for the Dirac, uniform, and exponential distributions. For the Dirac distribution case, it is shown that the model exhibits a Hopf bifurcation for certain values of the parameters involved in the system. As well, for these values, the structural stability of the SODE is studied, using the five KCC-invariants of the second-order canonical extension of the SODE, and all the cases prove to be Jacobi unstable.