Experimental continuation of limit cycle oscillations

Experimental continuation enables the reconstruction of the full bifurcation diagram of a nonlinear physical system without requiring a accurate mathematical model. This is typically achieved by combining feedback control-based methods and continuation procedures, allowing to trace both stable and unstable responses. This work focuses on the adaptation and application of such methods to autonomous systems, where the absence of external forcing poses a challenge in the estimation of the frequency of the response and in the contruction of the reference signal. The proposed adaptations are validated both numerically—on systems exhibiting Hopf and fold bifurcations—and experimentally, using an analog electronic Van der Pol-Duffing oscillator. In addition, a recent data-driven method for estimating the amplitude of unstable limit cycles from transient free-decay responses is experimentally validated. To account for the practical complexities of experimental implementation, a number of strategies are proposed and integrated, enabling the estimation procedure to be performed in real time within an online framework.