Intermittency Caused by Chaotic Modulation. II: --Lyapunov Exponent, Fractal Structure and Power Spectrum--

Abstract

A Mapping System under a chaotic modulation, which has the fixed point, independently of the control parameter and modulation, is studied both numerically and theoretically. When the fixed point becomes unstable as the control parameter is changed, the system generally associates with intermittency characteristics different from the Manneville-Pomeau type. Near the instability point the Lyapunov exponent and the power spectrum for the state variable exhibiting the intermittency are analyzed with the aid of the multiplicative noise model approximation introduced in the previous paper of this series. Theoretical results are found to agree well with numerical ones. Furthermore we discuss the transition from the two-dimensional attractor to the strange attractor with a fractal dimension.