CHAOTIC NETWORKS UNDER THRESHOLDING

2003 ◽  
Vol 17 (29) ◽  
pp. 5503-5524 ◽  
Author(s):  
SUDESHNA SINHA
Keyword(s):  
Spatiotemporal Chaos ◽  
Spatiotemporal Patterns ◽  
Control Algorithms ◽  
Electrical Circuits ◽  
Threshold Levels ◽  
Self Organized ◽  
Wide Range ◽  
Self Organized Criticality ◽  
Different Levels

We review some results on the phenomenology of networks of chaotic elements under threshold activated coupling. We show how thresholding at different levels gives rise to behaviour ranging from spatiotemporal cycles and spatiotemporal chaos, to scaling regimes reminiscent of self-organized criticality. We also indicate how our knowledge of the dynamical consequences of varying threshold levels can be used to design control algorithms targetting a wide range of spatiotemporal patterns. Some of these concepts are verified in experiments on chaotic electrical circuits.

scholarly journals Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

2016 ◽  
Author(s):  
Rene C. Batac ◽  
Antonino A. Paguirigan Jr. ◽  
Anjali B. Tarun ◽  
Anthony G. Longjas
Keyword(s):  
Probability Model ◽  
Single Parameter ◽  
Scaling Exponent ◽  
Cellular Automata Model ◽  
Critical Range ◽  
Self Organized ◽  
Proposed Model ◽  
Wide Range ◽  
Spatiotemporal Clustering ◽  
Self Organized Criticality

Abstract. We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of self-organized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy (magnitude) distributions closely follow power-law probability density functions (PDFs) with scaling exponent −5/3, consistent with the expectations of the Gutenberg–Richter (GR) law, for a wide range of the targeted-triggering probability values; this suggests that SOC mechanisms are still present in the model despite the introduction of the targeted triggering. Additionally, for targeted triggering probabilities within the range 0.004–0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, without disrupting the SOC properties of the sandpile grid. We believe that the critical targeting probability is a key requirement for SOC in seismicity, as it parametrizes the memory that is inherently present in earthquake-generating regions.

DYNAMICAL EXPLANATION FOR THE EMERGENCE OF POWER LAW IN A STOCK MARKET MODEL

1996 ◽  
Vol 07 (01) ◽  
pp. 65-72 ◽  
Author(s):  
MOSHE LEVY ◽  
SORIN SOLOMON ◽  
GIVAT RAM
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Wealth Distribution ◽  
Power Laws ◽  
Stationary Regime ◽  
Market Model ◽  
Self Organized ◽  
Wide Range ◽  
Self Organized Criticality ◽  
Sand Piles

Power laws are found in a wide range of different systems: From sand piles to word occurrence frequencies and to the size distribution of cities. The natural emergence of these power laws in so many different systems, which has been called self-organized criticality, seems rather mysterious and awaits a rigorous explanation. In this letter we study the stationary regime of a previously introduced dynamical microscopic model of the stock market. We find that the wealth distribution among investors spontaneously converges to a power law. We are able to explain this phenomenon by simple general considerations. We suggest that similar considerations may explain self-organized criticality in many other systems. They also explain the Levy distribution.

scholarly journals Universal Accretion Growth Using Sandpile Models

2015 ◽  
Vol 11 (S315) ◽  
Author(s):  
Srabani Datta ◽  
Ralph Spencer ◽  
Shane McKie
Keyword(s):  
Molecular Clouds ◽  
Velocity Structure ◽  
Power Law Distribution ◽  
Self Similarity ◽  
Scale Free ◽  
Fluid Turbulence ◽  
Self Organized ◽  
Wide Range ◽  
Self Organized Criticality ◽  
Sandpile Models

AbstractThe Bak Tang Weisenfeld (BTW) sandpile process is a model of a complex dynamical system with a large collection of particles or grains in a node that sheds load to their neighbours when they reach capacity. The cascades move around the system till it reaches stability with a critical point as an attractor. The BTW growth process shows self-organized criticality (SOC) with power- law distribution in cascade sizes having slope -5/3. This self-similarity of structure is synonymous with the fractal structure found in molecular clouds of Kolmogorov dimension 1.67 and by treating cascades as waves, scaling functions are found to be analogous to those observed for velocity structure functions in fluid turbulence. In this paper, we show that this is a naturally occuring universal process giving rise to scale - free structures with size limited only by the number of infalling grains. We also compare the BTW process with other sandpile models such as the Manna and Zhang processes. We find that the BTW sandpile model can be applied to a wide range of objects including molecular clouds, accretion disks and perhaps galaxies.

scholarly journals Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

2017 ◽  
Vol 24 (2) ◽  
pp. 179-187 ◽  
Author(s):  
Rene C. Batac ◽  
Antonino A. Paguirigan Jr. ◽  
Anjali B. Tarun ◽  
Anthony G. Longjas
Keyword(s):  
Probability Model ◽  
Single Parameter ◽  
Scaling Exponent ◽  
Cellular Automata Model ◽  
Critical Range ◽  
Self Organized ◽  
Proposed Model ◽  
Wide Range ◽  
Spatiotemporal Clustering ◽  
Self Organized Criticality

Abstract. We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of self-organized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy distributions closely follow power-law probability density functions (PDFs) with a scaling exponent of around −1. 6, consistent with the expectations of the Gutenberg–Richter (GR) law, for a wide range of the targeted triggering probability values. Additionally, for targeted triggering probabilities within the range 0.004–0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, the foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, while introducing minimal parameters in the simple rules of the sandpile. We believe that the critical targeting probability parameterizes the memory that is inherently present in earthquake-generating regions.

Problem behavior in autism spectrum disorders: A paradigmatic self-organized perspective of network structures

2019 ◽  
Vol 42 ◽  
Author(s):  
Lucio Tonello ◽  
Luca Giacobbi ◽  
Alberto Pettenon ◽  
Alessandro Scuotto ◽  
Massimo Cocchi ◽  
...  
Keyword(s):  
Autism Spectrum Disorder ◽  
Problem Behaviors ◽  
Autism Spectrum ◽  
The Self ◽  
Network Structures ◽  
Self Organized ◽  
Critical Equilibrium ◽  
Self Organized Criticality ◽  
Acute Agitation ◽  
Spectrum Disorders

AbstractAutism spectrum disorder (ASD) subjects can present temporary behaviors of acute agitation and aggressiveness, named problem behaviors. They have been shown to be consistent with the self-organized criticality (SOC), a model wherein occasionally occurring “catastrophic events” are necessary in order to maintain a self-organized “critical equilibrium.” The SOC can represent the psychopathology network structures and additionally suggests that they can be considered as self-organized systems.

Self-Organized Criticality in the Autowave Model of Speciation

2020 ◽  
Vol 75 (5) ◽  
pp. 398-408
Author(s):  
A. Y. Garaeva ◽  
A. E. Sidorova ◽  
N. T. Levashova ◽  
V. A. Tverdislov
Keyword(s):  
Self Organized ◽  
Self Organized Criticality

Modeling Extinction

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Evolutionary Biology ◽  
Large Scale ◽  
Competitive Exclusion ◽  
Applied Mathematics ◽  
Santa Fe ◽  
New Approach ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Extinction Events ◽  
Mass Extinction Events

Developed after a meeting at the Santa Fe Institute on extinction modeling, this book comments critically on the various modeling approaches. In the last decade or so, scientists have started to examine a new approach to the patterns of evolution and extinction in the fossil record. This approach may be called "statistical paleontology," since it looks at large-scale patterns in the record and attempts to understand and model their average statistical features, rather than their detailed structure. Examples of the patterns these studies examine are the distribution of the sizes of mass extinction events over time, the distribution of species lifetimes, or the apparent increase in the number of species alive over the last half a billion years. In attempting to model these patterns, researchers have drawn on ideas not only from paleontology, but from evolutionary biology, ecology, physics, and applied mathematics, including fitness landscapes, competitive exclusion, interaction matrices, and self-organized criticality. A self-contained review of work in this field.

Sign in / Sign up

Export Citation Format

Share Document