Sung-yool Choi and Eok-Kyun Lee

Department of Chemistry, Korea Advanced Institute of Science and Technology, 373-1 Kusung-dong Yusung-gu, Taejon 305-701 Republic of Korea

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 ¥ë near the transition point was determined in terms of the noise amplitude ¥ò and the correlation time ¥ó, and the critical exponent ¥á associated with ¥ó 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.