SCALING BEHAVIOR AT THE ONSET OF CHAOS IN THE LOGISTIC MAP DRIVEN BY COLORED NOISE

Abstract

The effects of additive colored noise near the onset of chaos have been studied for one-dimensional logistic maps. The scaling form of the Lyapunov exponent lambda near the transition point was determined in terms of the noise amplitude sigma and the correlation time tau, and the critical exponent alpha associated with tau was evaluated. Analysis shows that a certain approximation, which we call the effective white,noise approximation, followed by the renormalization group treatment, leads to essentially the same structure of the scaling function as that determined by the numerical method.