What can one learn about self-organized criticality from dynamical systems theory?

被引：32

作者：

Blanchard, P ^{[1
]}

Cessac, B

Krüger, T

机构：

[1] Univ Bielefeld, BiBoS, D-33501 Bielefeld, Germany

[2] Inst Non Lineaire Nice, F-06500 Valbonne, France

[3] Tech Univ Berlin, D-10623 Berlin, Germany

来源：

JOURNAL OF STATISTICAL PHYSICS | 2000年 / 98卷 / 1-2期

关键词：

self-organized criticality; hyperbolic dynamical systems; iterated functions systems;

D O I：

10.1023/A:1018639308981

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We develop a dynamical system approach for the Zhang model of self-organized criticality, for which the dynamics can be described either in terms of iterated function systems or as a piecewise hyperbolic dynamical system of skew-product type. In this setting we describe the SOC attractor. and discuss its fractal structure. We show how the Lyapunov exponents, the Haussdorf dimensions. and the system size are related to the probability distribution of the avalanche size via the Ledrappier-Young formula.

引用

页码：375 / 404

页数：30

共 38 条

[1] SELF-ORGANIZED CRITICALITY [J].

BAK, P ;

TANG, C ;

WIESENFELD, K .

PHYSICAL REVIEW A, 1988, 38 (01) :364-374

[2] SELF-ORGANIZED CRITICALITY - AN EXPLANATION OF 1/F NOISE [J].

BAK, P ;

TANG, C ;

WIESENFELD, K .

PHYSICAL REVIEW LETTERS, 1987, 59 (04) :381-384

[3]

BAK P, 1996, HOW NATURE WORKS

[4] SELF-ORGANIZATION AND ANOMALOUS DIFFUSION [J].

BANTAY, P ;

JANOSI, IM .

PHYSICA A, 1992, 185 (1-4) :11-18

[5]

Barnsley M. F., 2014, Fractals Everywhere

[6]

BECK C, 1993, CAMBRIDGE NONLINEAR, V4

[7] A dynamical system approach to SOC models of Zhang's type [J].

Blanchard, P ;

Cessac, B ;

Kruger, T .

JOURNAL OF STATISTICAL PHYSICS, 1997, 88 (1-2) :307-318

[8]

BLANCHARD P, UNPUB LYAPUNOV EXPON

[9]

BLANCHARD P, UNPUB ERGODICITY ONE

[10]

Bowen R., 1975, LECT NOTES MATH, V470

← 1 2 3 4 →