BISPECTRAL ANALYSIS OF POSSESSING CHAOTIC MOTION

Bispectral analyses of the equations producing a chaotic Rossler attractor and the chaotic trajectories of a one-mode Galerkin approximation of the magnetically buckled beam are presented, yielding interesting consequences concerning chaotic system identification for driven oscillators and autonomous systems. Bicoherence spectra isolate the phase coupling between increasing numbers of triads of Fourier modes for a pure period doubling sequence route to chaos for the Rossler equations. Bicoherences from a period doubling-intermittency catastrophe route to chaotic motion are also observed for single frequency excitation for the buckled beam. Although the bicoherence successfully characterizes important aspects of the non-linearity of the Rossler attractor in the nonchaotic and chaotic regimes, where the primary non-linearity is quadratic, it only partially characterizes the magnetically buckled beam system because the dominant non-linearity is cubic. © 1990.