Experimental continuation of periodic orbits through a fold

TL;DR

This paper introduces an experimental continuation method for tracking periodic orbits, including unstable ones, in physical systems by combining control techniques with Newton iterations, demonstrated on a forced pendulum.

Contribution

It presents a novel experimental approach to continue periodic orbits through bifurcations, including unstable branches, using a control-based setup.

Findings

Successfully continued stable and unstable periodic orbits in a forced pendulum

Demonstrated continuation through a fold bifurcation

Validated the method's effectiveness in experimental settings

Abstract

We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic orbit can be continued even when it is unstable. This is demonstrated with the continuation of initially stable rotations of a vertically forced pendulum experiment through a fold bifurcation to find the unstable part of the branch.