International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 51848, 15 pages
doi:10.1155/IJMMS/2006/51848
Linear and structural stability of a cell division
process model
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.
Abstract
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.