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 email@example.com
Published online: 15 September 1999
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.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 47.53.+n – Fractals
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999