BISPECTRAL ANALYSIS OF CHUA'S CIRCUIT

Abstract

Bispectral analysis (which isolates quadratic nonlinear interactions among triads of Fourier components) is used to investigate bifurcations in Chua's circuit. For period-doubled limit cycles, the dominant interactions of the circuit are quadratically nonlinear, and bicoherence spectra isolate the phase coupling between increasing numbers of triads of Fourier components as the nonlinearity of the system is increased. For circuit parameters that result in a chaotic, Rössler-type attractor, bicoherence spectra indicate that quadratic nonlinear interactions are important to the dynamics. For parameters that lead to the double scroll chaotic attractor the bispectrum is zero, suggesting that nonlinear interactions of order higher than quadratic dominate the dynamics. Higher-than-second order spectra (e.g. trispectra) are required to isolate the individual nonlinear interactions for the double scroll.