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