What can one learn about Self-Organized Criticality from Dynamical Systems theory ?
Blanchard, Ph. ; Cessac, B. ; Krueger, T.
HAL, inria-00529554 / Harvested from HAL
Text on HAL
We develop a dynamical system approach for the Zhang's 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 Hausdorff dimensions, and the system size are related to the probability distribution of the avalanche size, via the Ledrappier-Young formula.
Publié le : 2000-07-05
Classification:  [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD],  [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech],  [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 
@article{inria-00529554,
     author = {Blanchard, Ph. and Cessac, B. and Krueger, T.},
     title = {What can one learn about Self-Organized Criticality from Dynamical Systems theory ?},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/inria-00529554}
}

Blanchard, Ph.; Cessac, B.; Krueger, T. What can one learn about Self-Organized Criticality from Dynamical Systems theory ?. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/inria-00529554/