Detecting Stability and Bifurcation Points in Control-Based Continuation for a Physical Experiment of the Zeeman Catastrophe Machine

Feedback-based control of dynamical systems enables tracking of unstable branches that cannot be reached by the free evolution of a simulated or physical system. As the stationary points are stabilized with these control methods, the stability information on the original system gets lost in the data from the transient behavior reaching these equilibria. We introduce, by means of a physical experiment of the Zeeman catastrophe machine, a method to construct the whole bifurcation diagram including stability information about the underlying uncontrolled equilibria and the location of bifurcation points.