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
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
