Forecasting critical points and post-critical limit cycles in nonlinear oscillatory systems using pre-critical transient responses

A unique method for forecasting Hopf bifurcations and the complete post-bifurcation dynamics of nonlinear oscillatory systems is proposed. The method is model-less and uses measurements of the system only in the pre-bifurcation regime. The forecasts are three-dimensional bifurcation diagrams using a few measurements of the system response to perturbations in the pre-bifurcation regime. To demonstrate the forecasting method and its advantages, it is employed to predict bifurcation diagrams of a 3-DOF fluid-structural system. Surrogate measurement data is obtained from simulations and used as input for the forecasting algorithm. Results show that the bifurcation diagrams are forecasted accurately in both supercritical and subcritical bifurcations. The method accurately forecasts the bifurcation point, the bifurcation type and the post-bifurcation limit cycle amplitudes despite the fact that only pre-bifurcation regime data are used for forecasting.