Intermittency Caused By Chaotic Modulation. III: Self-Similarity and Higher Order Correlation Functions

Abstract

The power law decay of the time correlation immediately after the intermittency transition associated with the instability of the fixed point under chaotic modulation is studied in an extended way from the viewpoint of the self-similarity of the time sequence of the intermittency variable rt. The self-similarity Ansatz leads to the power law behavior of moments of time-scale dependent average A(t)(≡t-1\intt0rsds), i.e., ≪[A(t)]q>∝t-qλq, (q>0), t being a certain intermediate time scale. The exponent λq turns out to be insensitive on details of systems, and the thoretical result λq=(1-1/q)/2 is found to be in good agreement with numerical results for three differnt systems. This suggests that λq is a universal function characterizing the self-similarity of the intermittency caused by chaotic modulation.