# Lyapunov exponents and transport in the Zhang model of self-organized criticality

Cessac B, Blanchard P, Krüger T (2001)

PHYSICAL REVIEW E 64(1).

*Journal Article*|

*Published*|

*English*

No fulltext has been uploaded

Author

Abstract

We discuss the role played by Lyapunov exponents in the dynamics of Zhang's model of self-organized criticality. We show that a Large part of the spectrum (the slowest modes) is associated with energy transport in the lattice. In particular, we give bounds on the first negative Lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time. We then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites. We use a finite size scaling ansatz for the Lyapunov spectrum, and relate the scaling exponent to the scaling of quantities such as avalanche size, duration, density of active sites, etc.

Publishing Year

ISSN

eISSN

PUB-ID

### Cite this

Cessac B, Blanchard P, Krüger T. Lyapunov exponents and transport in the Zhang model of self-organized criticality.

*PHYSICAL REVIEW E*. 2001;64(1).Cessac, B., Blanchard, P., & Krüger, T. (2001). Lyapunov exponents and transport in the Zhang model of self-organized criticality.

*PHYSICAL REVIEW E*,*64*(1).Cessac, B., Blanchard, P., and Krüger, T. (2001). Lyapunov exponents and transport in the Zhang model of self-organized criticality.

*PHYSICAL REVIEW E*64.Cessac, B., Blanchard, P., & Krüger, T., 2001. Lyapunov exponents and transport in the Zhang model of self-organized criticality.

*PHYSICAL REVIEW E*, 64(1). B. Cessac, P. Blanchard, and T. Krüger, “Lyapunov exponents and transport in the Zhang model of self-organized criticality”,

*PHYSICAL REVIEW E*, vol. 64, 2001. Cessac, B., Blanchard, P., Krüger, T.: Lyapunov exponents and transport in the Zhang model of self-organized criticality. PHYSICAL REVIEW E. 64, (2001).

Cessac, B, Blanchard, Philippe, and Krüger, Tyll. “Lyapunov exponents and transport in the Zhang model of self-organized criticality”.

*PHYSICAL REVIEW E*64.1 (2001).
This data publication is cited in the following publications:

This publication cites the following data publications:

### 4 Citations in Europe PMC

Data provided by Europe PubMed Central.

Perception and self-organized instability.

Friston K, Breakspear M, Deco G.,

PMID: 22783185

Friston K, Breakspear M, Deco G.,

*Front Comput Neurosci*6(), 2012PMID: 22783185

Asymptotic behavior and synchronizability characteristics of a class of recurrent neural networks.

Cebulla C.,

PMID: 17650067

Cebulla C.,

*Neural Comput*19(9), 2007PMID: 17650067

Dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect: chaos, turbulence, and band propagation.

Ananthakrishna G, Bharathi MS.,

PMID: 15447549

Ananthakrishna G, Bharathi MS.,

*Phys Rev E Stat Nonlin Soft Matter Phys*70(2 Pt 2), 2004PMID: 15447549

Anomalous scaling and Lee-Yang zeros in self-organized criticality.

Cessac B, Meunier JL.,

PMID: 11909189

Cessac B, Meunier JL.,

*Phys Rev E Stat Nonlin Soft Matter Phys*65(3 Pt 2A), 2002PMID: 11909189

### 28 References

Data provided by Europe PubMed Central.

The distribution of Lyapunov exponents: Exact results for random matrices

Newman,

Newman,

*Communications in Mathematical Physics*103(1), 1986
The Metric Entropy of Diffeomorphisms: Part I: Characterization of Measures Satisfying Pesin's Entropy Formula

Ledrappier,

Ledrappier,

*Annals of Mathematics*122(3), 1985
A dynamical system approach to SOC models of Zhang's type

Blanchard,

Blanchard,

*Journal of Statistical Physics*88(1-2), 1997### Export

0 Marked Publications### Web of Science

View record in Web of Science®### Sources

PMID: 11461357

PubMed | Europe PMC