Complexity and Criticality

2020 ◽  
pp. 42-50
Author(s):  
Helmut Satz
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
Critical Point ◽  
Correlation Length ◽  
Critical Behavior ◽  
Scale Free ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Free Behavior

Complex systems and critical behavior in complex system are defined in terms of correlation between constituents in the medium, subject to screening by intermediate constituents. At a critical point, the correlation length diverges—as a result, one finds the scale-free behavior also observed for bird flocks. This behavior is therefore possibly a form of self-organized criticality.

scholarly journals Observational evidence in favor of scale-free evolution of sunspot groups

2018 ◽  
Vol 618 ◽  
pp. A183
Author(s):  
A. Shapoval ◽  
J.-L. Le Mouël ◽  
M. Shnirman ◽  
V. Courtillot
Keyword(s):  
Weibull Distribution ◽  
Power Law ◽  
Large Range ◽  
Scale Free ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Spatio Temporal ◽  
Computational Procedures ◽  
Definition Of ◽  
Sunspot Groups

Context. The hypothesis stating that the distribution of sunspot groups versus their size (φ) follows a power law in the domain of small groups was recently highlighted but rejected in favor of a Weibull distribution. Aims. In this paper we reconsider this question, and are led to the opposite conclusion. Methods. We have suggested a new definition of group size, namely the spatio-temporal “volume” (V) obtained as the sum of the observed daily areas instead of a single area associated with each group. Results. With this new definition of “size”, the width of the power-law part of the distribution φ ∼ 1/Vβ increases from 1.5 to 2.5 orders of magnitude. The exponent β is close to 1. The width of the power-law part and its exponent are stable with respect to the different catalogs and computational procedures used to reduce errors in the data. The observed distribution is not fit adequately by a Weibull distribution. Conclusions. The existence of a wide 1/V part of the distribution φ suggests that self-organized criticality underlies the generation and evolution of sunspot groups and that the mechanism responsible for it is scale-free over a large range of sizes.

Criticality: How Changes Preserve Stability in Self-Organizing Systems

2018 ◽  
Vol 40 (11) ◽  
pp. 1613-1629 ◽  
Author(s):  
Philippe Accard
Keyword(s):  
Complex System ◽  
System Theory ◽  
Social Systems ◽  
Theoretical Framework ◽  
Fundamental Issue ◽  
Self Organized ◽  
Self Organized Criticality ◽  
New Treatment ◽  
Over Time ◽  
Self Organizing

Self-organizing systems are social systems which are immanently and constantly recreated by agents. In a self-organizing system, agents make changes while preserving stability. If they do not preserve stability, they push the system toward chaos and cannot recreate it. How changes preserve stability is thus a fundamental issue. In current works, changes preserve stability because agents’ ability to make changes is limited by interaction rules and power. However, how agents diffuse the changes throughout the system while preserving its stability has not been addressed in these works. We have addressed this issue by borrowing from a complex system theory neglected thus far in organization theories: self-organized criticality theory. We suggest that self-organizing systems are in critical states: agents have equivalent ability to make changes, and none are able to foresee or control how their changes diffuse throughout the system. Changes, then, diffuse unpredictably – they may diffuse to small or large parts of the system or not at all, and it is this unpredictable diffusion that preserves stability in the system over time. We call our theoretical framework self-organiz ing criticality theory. It presents a new treatment of change and stability and improves the understanding of self-organizing.

SELF-ORGANIZED CRITICALITY IN AN ASEXUAL MODEL?

2000 ◽  
Vol 11 (06) ◽  
pp. 1257-1262 ◽  
Author(s):  
COLIN CHISHOLM ◽  
NAEEM JAN ◽  
PETER GIBBS ◽  
AYŞE ERZAN
Keyword(s):  
Steady State ◽  
Recent Work ◽  
Critical Behavior ◽  
Critical State ◽  
Small Perturbations ◽  
Sandpile Model ◽  
Self Organized ◽  
Search For Self ◽  
Self Organized Criticality

Recent work has shown that the distribution of steady state mutations for an asexual "bacteria" model has features similar to that seen in Self-Organized Critical (SOC) sandpile model of Bak et al. We investigate this coincidence further and search for "self-organized critical" state for bacteria but instead find that the SOC sandpile critical behavior is very sensitive; critical behavior is destroyed with small perturbations effectively when the absorption of sand is introduced. It is only in the limit when the length of the genome of the bacteria tends to infinity that SOC properties are recovered for the asexual model.

SELF-ORGANIZED CRITICALITY IN AN EARTHQUAKE MODEL BASED ON ASSORTATIVE SCALE-FREE NETWORKS

2011 ◽  
Vol 22 (05) ◽  
pp. 483-493 ◽  
Author(s):  
MIN LIN ◽  
GANG WANG
Keyword(s):  
Stress Evolution ◽  
Scale Invariant ◽  
Avalanche Size ◽  
Scale Free ◽  
Self Organized ◽  
Dynamical Behaviors ◽  
Period Distribution ◽  
Scale Free Networks ◽  
Earthquake Model ◽  
Self Organized Criticality

A modified Olami–Feder–Christensen (OFC) earthquake model on scale-free networks with assortative mixing is introduced. In this model, the distributions of avalanche sizes and areas display power-law behaviors. It is found that the period distribution of avalanches displays a scale-invariant law with the increment of range parameter d. More importantly, different assortative topologies lead to different dynamical behaviors, such as the distribution of avalanche size, the stress evolution process, and period distribution.

SELF-ORGANIZED CRITICAL BEHAVIOR OF TWO-DIMENSIONAL FOAMS

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 339-348 ◽  
Author(s):  
KYOZI KAWASAKI ◽  
TOHRU OKUZONO
Keyword(s):  
Surface Tension ◽  
Computer Simulation ◽  
Critical Behavior ◽  
Applied Strain ◽  
Two Dimensional ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Simple Dynamical Model ◽  
Earthquake Models ◽  
Foam Rheology

A simple dynamical model for two-dimensional dry foam rheology is constructed for which surface tension effects and viscous dissipation at Plateau borders (intersections of three cell boundaries) are taken into account and is studied by computer simulation. Under externally applied shear strain increasing at small rates, the system exhibits avalanche-like release of stress that has been accumulating under increasing strain. There is a close similarity with earthquake models that show self-organized criticality (SOC). We discuss related simulation of two-dimensional wet foams under statically applied strain by Hutzler et al. [Phil. Mag. B71, 277 (1995)] showing critical behavior.

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