Chaos control using noise

The mechanism and the characteristics of the appearance of order on chaos with Gaussian white noise are investigated in the one-dimensional return map of the Belousov–Zhabotinsky chaos. This order (noise-induced order) appears as the constancy of the topological entropy and the decrease of the Kolmogorov entropy. Analysis of the five-times iterated return map reveals that “noise-induced order” is caused by the increase of the length of the laminar region and the subsequent change of the invariant density, where noise generates the stable point on the diagonal. We also find that “noise-induced order” is accelerated with an increase of the noise period.