Forecasting bifurcations in parametrically excited systems

Forecasting bifurcations in parametrically excited systems before they occur is an active area of research both for engineered and natural systems. In particular, anticipating the distance to critical transitions, and predicting the state of the system after such transitions, remains a challenge, especially when there is an explicit time input to the system. In this work, a new model-less method is presented to address these challenges based on monitoring transient recoveries from large perturbations in the pre-bifurcation regime. Recoveries are studied in a Poincaré section to address the challenge caused by explicit time input. Both numerical and experimental results are presented to demonstrate the proposed technique. A discussion of the accuracy of the proposed approach is included also.