A Transient-State Analysis of Tyson's Model for the Cell Division Cycle by Means of KCC-Theory

The transient-state stability analysis for the trajectories of Tyson's equations for the cell-division cycle is given by the so-called KCC-Theory. This is the differential geometric theory of the variational equations for deviation of whole trajectories to nearby ones. The relationship between Lyapunov stability of steady-states and limit cycles is throughly examined. We show that the region of stability (where, in engineering parlance, the system is “hunting”) encloses the Tyson limit cycle, while outside this region the trajectories exhibit aperiodic behaviour.