Cheating Nyquist: Nonlinear model reconstruction with undersampled frequency response of a forced, damped, nonlinear oscillator

This paper investigates the potential for using inverse techniques based on frequency and amplitude response for model reconstruction of systems perturbed by forced oscillations. The paradigm system of the Duffing oscillator, which exhibits forced damped nonlinear oscillations, is used to demonstrate the utility of frequency and amplitude response for optimal parameter estimation. The formalism developed here is used to infer multiple parameters from a chaotic time series, and to estimate accurately a damping time scale faster than the sampling rate. For linear systems, this is classically disallowed from the Nyquist-Shannon sampling theorem. Yet, with the nonlinear response balancing damping and nonlinearity, the fast time scale can be estimated using inverse techniques with very coarse sampling. The latter is an important property for the target applications in systems biology, where transcriptomic and proteomic data acquisition is expensive.