Global stability and Hopf bifurcation of a three-component model for cell production systems

Abstract

The dynamics of a three-component model for hierarchical cell production systems regulated by the level of mature cells is considered. Our model is based on a multi-component model, a collection of ordinary differential equations which rely on a mechanism of external signals feedback. We analyze the existence and global stability of non-negative equilibria. We obtain the existence of Hopf bifurcation, and the direction and stability of bifurcating periodic orbits are calculated. Numerical simulations are included to show the rich spatiotemporal dynamics.