I have recently come up with a method for tracking limit-point bifurcations directly in the experiment. The approach combines data regression techniques to identify bifurcation points and control-based continuation (CBC) to track their evolution as parameters (such as the forcing frequency) are varied. The method was successfully demonstrated on nonlinear oscillator with a softening-hardening stiffness characteristic (Figure 1).
A paper describing the method in details has been recently accepted for publication in the Journal of Bifurcation and Chaos. The final version submitted to the journal can be found here. My collaborators on this project were David Barton and Simon Neild.