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

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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 r_t. The self-similarity Ansatz leads to the power law behavior of moments of time-scale dependent average A(t)(≡t^<-1>∫^t_0r_sds), i.e., <[A(t)]^q>∝t^<-qλq>, (q>0), t being a certain intermediate time scale. The exponent λ_q turns out to be insensitive on details of systems, and the theoretical result λ_q=(1-1/q)/2 is found to be in good agreement with numerical results for three different systems. This suggests that λ_q is a universal function characterizing the self-similarity of the intermittency caused by chaotic modulation.
理論物理学刊行会の論文
1987-05-25