Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.