Resonant chaos control by periodic perturbations

Abstract

The method of resonant chaos control by periodic perturbations is discussed and applied to a model of chemical chaos. Resonant chaos control converts chaotic into periodic motion by imposing one or more sinusoidal perturbation functions. The frequencies, phases and amplitudes of the driving functions are adjusted appropriately. As a novelty we use the cross-correlation function to compare the results of the resonant chaos control with that of the Pyragas method in which an unstable periodic orbit is stabilized by time-delayed feedback. From the appearance of the frequencies in the chaotic Fourier spectra it is possible to approximately predict that the type of unstable periodic orbit which is most readily stabilized belongs to the periodic window closest to the chaotic state. The simple perturbation method is convenient to apply to experimental systems such as chemical chaos. The 7-variable model (Montanator) of Györgyi and Field with the boundary conditions of a continuous flow reactor is used in the simulations.