Stability of Hopf Bifurcation in Quasi-Linear Models

The purpose of the paper is to give explicit conditions for the stability analysis of the Hopf bifurcation in quasi-linear models. Models of this kind are most often met in population dynamics and biochemical kinetics. The considered approach calls into play auxiliary linear control systems. The stability of the Hopf bifurcation is determined through the transfer functions of these systems. Models of an artificially cultivated cell population and a cyclic epidemics model are investigated by the method.