Extended Self-Similarity in Modulational Intermittency Based on the Continuous-Time Random Walk Approach

Abstract

Anomalous diffusion caused by modulational intermittency, which is also known as on-off intermittency, is studied on the basis of the continuous-time random walk (CTRW) approach. There exists a characteristic time scale τ . For the time region t � τ , anomalous subdiffusion is observed, which is followed by normal diffusion for t � τ . Higher-order moments are analytically obtained by use of the saddle-point method, and it is found that they obey scaling relations that are reminiscent of extended self-similarity (ESS) and generalized extended selfsimilarity (GESS) found in turbulent systems. The results are compared with those obtained using the numerical inverse Laplace transform and from model simulations employing a coupled chaotic map. Good agreement between these results is obtained even for lowerorder moments.