Controlling of chaotic motion by chaos and noise signals in a logistic map and a Bonhoeffer–van der Pol oscillator

The possibility of the conversion of a chaotic attractor to a strange but nonchaotic attractor is investigated numerically in both a discrete system, the logistic map, and in a continuous dynamical system, the Bonhoeffer--van der Pol oscillator. A suppression of the chaotic property, namely, the sensitive dependence on initial states, is found when an appropriate (i) chaotic signal and (ii) Gaussian white noise are added. A strange but nonchaotic attractor is shown to occur for some ranges of amplitude of the external perturbation. The controlled orbit is characterized by the Lyapunov exponent, correlation dimension, power spectrum, and return map.