Eur. Phys. J. B 11, 345-360 (1999)
https://doi.org/10.1007/s100510050944

Multi-affinity and multi-fractality in systems of chaotic elements with long-wave forcing

Department of Physics, Graduate School of Sciences, Kyoto University, Kyoto 606-8502, Japan

Corresponding author: ^a nakao@ton.scphys.kyoto-u.ac.jp

Received: 16 November 1998
Published online: 15 September 1999

Abstract

Multi-scaling properties in quasi-continuous arrays of chaotic maps driven by long-wave random force are studied. The spatial pattern of the amplitude X(x,t) is characterized by multi-affinity, while the field defined by its coarse-grained spatial derivative exhibits multi-fractality. The strong behavioral similarity of the X- and Y-fields respectively to the velocity and energy dissipation fields in fully-developed fluid turbulence is remarkable, still our system is unique in that the scaling exponents are parameter-dependent and exhibit nontrivial q-phase transitions. A theory based on a random multiplicative process is developed to explain the multi-affinity of the X-field, and some attempts are made towards the understanding of the multi-fractality of the Y-field.