Nonlinear characterization of a Rossler system under periodic closed-loop control via time-frequency and bispectral analysis

This study has two primary objectives; they are to investigate the nonlinear interactions (or quadratic phase-coupling) in a chaotic Rossler system under periodic closed-loop control via wavelet bispectral analysis; and to further identify the component mechanisms of synchronization. It is observed that a fixed-gain, fixed-frequency controller produces quadratic phase-coupling and decoupling along lines of constant frequency and that are perpendicular to the diagonal of the bicoherence matrix. Further, it was also observed that for synchronization to occur, both frequency entrainment and quadratic phase-coupling must be present. It was found that forcing the Rossler system with a constant frequency did not reduce the amplitude of the resulting period-1 orbit at sufficiently high gains. For the controller with a fixed gain and time-varying error signal, it was found that the time varying forcing frequency (adjusted by an extremum seeking feedback loop) linearizes the Rossler system and in doing so, suppresses the phase coherence completely. The time-varying forcing frequency removes the conditions for frequency entrainment by providing broadband attenuation; the result is suppression without synchronization.