Prediction of long-term dynamics from transients

Existing methods of time series analysis of nonlinear dynamical systems deal with the dynamics on single (strange) attractors. We extend this method for systems that can be externally manipulated. We interact with a previously unknown system by perturbing it randomly and recording the responses. By following transients for a short time and approximating the global flow, we can predict the final long-term dynamics, including coexisting multistable, chaotic, or periodic dynamics. Also the localization of basins of attraction is possible, enabling the selection or control of the type of final dynamics. Numerical and experimental examples of driven nonlinear oscillators are given.