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

H. Nakao () and Y. Kuramoto

The European Physical Journal B: Condensed Matter and Complex Systems, 1999, vol. 11, issue 2, 345-360

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 Y(x, t) := |(X(x + δ, t) − X(x, t))/δ| 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. Copyright Società Italiana di Fisica, Springer-Verlag 1999

Keywords: PACS. 05.45.-a Nonlinear dynamics and nonlinear dynamical systems; 47.53.+n Fractals (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/BF03219173

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