Slow passage through a supercritical Hopf bifurcation: Time-delayed response in the Belousov–Zhabotinsky reaction in a batch reactor

Abstract

When the control parameter of a dynamical system varies continuously, bifurcation is delayed due to the inertia in the system’s response. We study experimentally the time delay of the supercritical Hopf bifurcation that arises from the parametric drift of the oscillating Belousov–Zhabotinsky reaction under batch conditions. The time-dependent oscillation amplitude and period are analyzed using the normal form of the supercritical Hopf bifurcation with a time-dependent control parameter. We show that this approach describes the time evolution of the entire oscillatory domain from high amplitude to vanishing oscillations.