Comparative Analysis of Biological Networks by Control Theoretic Methods

Abstract: This project deals with two Goodwin models of circadian rythms and three reduced models in understanding the Belousov-Zhabotinski models of chemical reaction. They are examined and compared by applying dynamical systems theory and control theoretical tools. More precisely, stability analysis of equilibria and the Hopf bifurcations. Moreover, we investigate the issues such as positivity and boundeness of the trajectories. Some are carried out by mathematical analysis and some are carried out by numerical simulations performed by Matlab. In particular, we provide a complete parameter description on stability of the Goodwin model in terms of the Hill number, which seems non-addressed in the literature.