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 voltag es 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 intera ctions between triads and quartets of Fourier components that govern the pr ocess dynamics are modeled accurately. For parameters that produce the doub le-scroll attractor, both measured and modeled time series have small bispe ctra, but nonzero trispectra, consistent with higher-than-second order nonl inearities dominating the chaos.