scholarly journals SELF-ORGANIZED CRITICALITY IN A MODEL OF COLLECTIVE BANK BANKRUPTCIES

2002 ◽  
Vol 13 (03) ◽  
pp. 333-341 ◽  
Author(s):  
AGATA ALEKSIEJUK ◽  
JANUSZ A. HOŁYST ◽  
GUEORGI KOSSINETS
Keyword(s):  
Financial Market ◽  
Percolation Theory ◽  
Bank Failure ◽  
Directed Percolation ◽  
Power Law Distribution ◽  
Self Organized ◽  
Banking Networks ◽  
Self Organized Criticality ◽  
The Difference ◽  
2D And 3D

The question we address here is of whether phenomena of collective bankruptcies are related to self-organized criticality. In order to answer it we propose a simple model of banking networks based on the random directed percolation. We study effects of one bank failure on the nucleation of contagion phase in a financial market. We recognize the power law distribution of contagion sizes in 3d- and 4d-networks as an indicator of SOC behavior. The SOC dynamics was not detected in 2d-lattices. The difference between 2d- and 3d- or 4d-systems is explained due to the percolation theory.

Modeling Research on Spatiotemporal Dynamics of the Hippocampus

1997 ◽  
Vol 07 (01) ◽  
pp. 187-198 ◽  
Author(s):  
Haijian Sun ◽  
Lin Liu ◽  
Chunhua Feng ◽  
Aike Guo
Keyword(s):  
Pyramidal Cells ◽  
Behavioral Pattern ◽  
Spatiotemporal Dynamics ◽  
Epileptic Focus ◽  
Power Law Distribution ◽  
Ca1 Pyramidal Cells ◽  
Self Organized ◽  
Hippocampal Ca1 ◽  
Self Organized Criticality ◽  
Neurological Insult

The spatiotemporal dynamics of the hippocampus is studied. We first propose a fractal algorithm to model the growth of hippocampal CA1 pyramidal cells, together with an avalanche model for information transmission. Then the optical records of an epileptic focus in the hippocampus are analyzed and simulated. These processes indicate that the hippocampus normally stays in self-organized criticality with a harmonious spatiotemporal behavioral pattern, that is, showing 1/f fluctuation and power law distribution. In case of a neurological insult, the hippocampal system may step into supercriticality and initiate epilepsy.

SELF-ORGANIZED CRITICALITY MODEL FOR EARTHQUAKES: QUIESCENCE, FORESHOCKS AND AFTERSHOCKS

1999 ◽  
Vol 09 (12) ◽  
pp. 2249-2255 ◽  
Author(s):  
S. HAINZL ◽  
G. ZÖLLER ◽  
J. KURTHS
Keyword(s):  
Power Law ◽  
B Value ◽  
Power Law Distribution ◽  
Aftershock Activity ◽  
Omori Law ◽  
Self Organized ◽  
Spatiotemporal Clustering ◽  
Self Organized Criticality ◽  
Clustering Of Events ◽  
Foreshock Activity

We introduce a crust relaxation process in a continuous cellular automaton version of the Burridge–Knopoff model. Analogously to the original model, our model displays a robust power law distribution of event sizes (Gutenberg–Richter law). The principal new result obtained with our model is the spatiotemporal clustering of events exhibiting several characteristics of earthquakes in nature. Large events are accompanied by a precursory quiescence and by localized fore- and aftershocks. The increase of foreshock activity as well as the decrease of aftershock activity follows a power law (Omori law) with similar exponents p and q. All empirically observed power law exponents, the Richter B-value, p and q and their variability can be reproduced simultaneously by our model, which depends mainly on the level of conservation and the relaxation time.

scholarly journals Transition from Self-Organized Criticality into Self-Organization during Sliding Si3N4 Balls against Nanocrystalline Diamond Films

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1055
Author(s):  
Bogatov ◽  
Podgursky ◽  
Vagiström ◽  
Yashin ◽  
Shaikh ◽  
...  
Keyword(s):  
Friction Force ◽  
Power Law ◽  
Early Stage ◽  
Nanocrystalline Diamond ◽  
The Self ◽  
Self Organization ◽  
Power Law Distribution ◽  
Reciprocating Sliding ◽  
Self Organized ◽  
Self Organized Criticality

The paper investigates the variation of friction force (Fx) during reciprocating sliding tests on nanocrystalline diamond (NCD) films. The analysis of the friction behavior during the run-in period is the focus of the study. The NCD films were grown using microwave plasma-enhanced chemical vapor deposition (MW-PECVD) on single-crystalline diamond SCD(110) substrates. Reciprocating sliding tests were conducted under 500 and 2000 g of normal load using Si3N4 balls as a counter body. The friction force permanently varies during the test, namely Fx value can locally increase or decrease in each cycle of sliding. The distribution of friction force drops (dFx) was extracted from the experimental data using a specially developed program. The analysis revealed a power-law distribution f-µ of dFx for the early stage of the run-in with the exponent value (µ) in the range from 0.6 to 2.9. In addition, the frequency power spectrum of Fx time series follows power-law distribution f-α with α value in the range of 1.0–2.0, with the highest values (1.6–2.0) for the initial stage of the run-in. No power-law distribution of dFx was found for the later stage of the run-in and the steady-state periods of sliding with the exception for periods where a relatively extended decrease of coefficient of friction (COF) was observed. The asperity interlocking leads to the stick-slip like sliding at the early stage of the run-in. This tribological behavior can be related to the self-organized criticality (SOC). The emergence of dissipative structures at the later stages of the run-in, namely the formation of ripples, carbonaceous tribolayer, etc., can be associated with the self-organization (SO).

Self-Organized Critical Models

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Computer Simulations ◽  
Power Law ◽  
Large Scale ◽  
Fitness Landscape ◽  
Fitness Landscapes ◽  
Power Law Distribution ◽  
Edge Of Chaos ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Phenotype Space

The models discussed in the last chapter are intriguing, but present a number of problems. In particular, most of the results about them come from computer simulations, and little is known analytically about their properties. Results such as the power-law distribution of extinction sizes and the system's evolution to the "edge of chaos" are only as accurate as the simulations in which they are observed. Moreover, it is not even clear what the mechanisms responsible for these results are, beyond the rather general arguments that we have already given. In order to address these shortcomings, Bak and Sneppen (1993; Sneppen et al. 1995; Sneppen 1995; Bak 1996) have taken Kauffman's ideas, with some modification, and used them to create a considerably simpler model of large-scale coevolution which also shows a power-law distribution of avalanche sizes and which is simple enough that its properties can, to some extent, be understood analytically. Although the model does not directly address the question of extinction, a number of authors have interpreted it, using arguments similar to those of section 1.2.2.5, as a possible model for extinction by biotic causes. The Bak-Sneppen model is one of a class of models that show "self-organized criticality," which means that regardless of the state in which they start, they always tune themselves to a critical point of the type discussed in section 2.4, where power-law behavior is seen. We describe self-organized criticality in more detail in section 3.2. First, however, we describe the Bak-Sneppen model itself. In the model of Bak and Sneppen there are no explicit fitness landscapes, as there are in NK models. Instead the model attempts to mimic the effects of landscapes in terms of "fitness barriers." Consider figure 3.1, which is a toy representation of a fitness landscape in which there is only one dimension in the genotype (or phenotype) space. If the mutation rate is low compared with the time scale on which selection takes place (as Kauffman assumed), then a population will spend most of its time localized around a peak in the landscape (labeled P in the figure).

scholarly journals Self-organized criticality in solar flares: a cellular automata approach

2010 ◽  
Vol 17 (4) ◽  
pp. 339-344 ◽  
Author(s):  
L. F. Morales ◽  
P. Charbonneau
Keyword(s):  
Solar Flares ◽  
Electrical Current ◽  
Power Law Distribution ◽  
Additional Energy ◽  
Self Organized ◽  
Anisotropic Lattice ◽  
Self Organized Criticality ◽  
Released Energy ◽  
The Mean ◽  
Electrical Current Density

Abstract. We give an overview of a novel lattice-based avalanche model that reproduces well a number of observed statistical properties of solar flares. The anisotropic lattice is defined as a network of vertically-connected nodes subjected to horizontal random displacements mimicking the kinks introduced by random motions of the photospheric footpoints of magnetic fieldlines forming a coronal loop. We focus here on asymmetrical driving displacements, which under our geometrical interpretation of the lattice correspond to a net direction of twist of the magnetic fieldlines about the loop axis. We show that a net vertical electrical current density does build up in our lattice, as one would expect from systematic twisting of a loop-like magnetic structure, and that the presence of this net current has a profound impact on avalanche dynamics. The presence of an additional energy reservoir tends to increase the mean energy released by avalanches, and yield a probability distribution of released energy in better agreement with observational inferences than in its absence. Symmetrical driving displacements are in better conceptual agreement with a random shuffling of photospheric footpoint, and yield a power-law distribution of energy release with exponent larger than 2, as required in Parker's nanoflare model of coronal heating. On the other hand, moderate asymmetrical driving generate energy distribution exponents that are similar to those obtained from SOHO EUV observations.

scholarly journals Self-organized criticality and directed percolation

1999 ◽  
Vol 32 (14) ◽  
pp. 2633-2644 ◽  
Author(s):  
Alexei Vázquez ◽  
Oscar Sotolongo Costa
Keyword(s):  
Directed Percolation ◽  
Self Organized ◽  
Self Organized Criticality

scholarly journals Noise-Induced Spiral Waves in Astrocyte Syncytia Show Evidence of Self-Organized Criticality

1998 ◽  
Vol 79 (2) ◽  
pp. 1098-1101 ◽  
Author(s):  
Peter Jung ◽  
Ann Cornell-Bell ◽  
Kathleen Shaver Madden ◽  
Frank Moss
Keyword(s):  
Power Law ◽  
Spiral Waves ◽  
Power Law Distribution ◽  
Self Organized ◽  
Show Evidence ◽  
Self Organized Criticality ◽  
Chemical Waves ◽  
Cultured Networks ◽  
The Waves ◽  
Vertebrate Central Nervous System

Jung, Peter, Ann Cornell-Bell, Kathleen Shaver Madden, and Frank Moss. Noise-induced spiral waves in astrocyte syncytia show evidence of self-organized criticality. J. Neurophysiol. 79: 1098–1101, 1998. Long range (a few centimeters), long lived (many seconds), spiral chemical waves of calcium ions (Ca2+) are observed in cultured networks of glial cells for normal concentrations of the neurotransmitter kainate. A new method for quantitatively measuring the spatiotemporal size of the waves is described. This measure results in a power law distribution of wave sizes, meaning that the process that creates the waves has no preferred spatial or temporal (size or lifetime) scale. This power law is one signature of self-organized critical phenomena, a class of behaviors found in many areas of science. The physiological results for glial networks are fully supported by numerical simulations of a simple network of noisy, communicating threshold elements. By contrast, waves observed in astrocytes cultured from human epileptic foci exhibited radically different behavior. The background random activity, or “noise”, of the network is controlled by the kainate concentration. The mean rate of wave nucleation is mediated by the network noise. However, the power law distribution is invariant, within our experimental precision, over the range of noise intensities tested. These observations indicate that spatially and temporally coherent Ca2+ waves, mediated by network noise may play and important role in generating correlated neural activity (waves) over long distances and times in the healthy vertebrate central nervous system.

scholarly journals Self-Organized Criticality of Traffic Flow: There is Nothing Sweet about the Sweet Spot

2021 ◽  
Author(s):  
Jorge Laval
Keyword(s):  
Traffic Flow ◽  
Initial Conditions ◽  
Critical Density ◽  
Basic Unit ◽  
Power Law Distribution ◽  
Fundamental Diagram ◽  
Brownian Excursion ◽  
Self Organized ◽  
Time Space ◽  
Self Organized Criticality

This paper shows that the kinematic wave model exhibits self-organized criticality when initialized with random initial conditions around the critical density. A direct consequence is that conventional traffic management strategies seeking to maximize the flow may be detrimental as they make the system more unpredictable and more prone to collapse. Other implications for traffic flow in the capacity state are discussed, such as: \item jam sizes obey a power-law distribution with exponents 1/2, implying that both its mean and variance diverge to infinity, and therefore traditional statistical methods fail for prediction and control, \item the tendency to be at the critical state is an intrinsic property of traffic flow driven by our desire to travel at the maximum possible speed, \item traffic flow in the critical region is chaotic in that it is highly sensitive to initial conditions, \item aggregate measures of performance are proportional to the area under a Brownian excursion, and therefore are given by different scalings of the Airy distribution, \item traffic in the time-space diagram forms self-affine fractals where the basic unit is a triangle, in the shape of the fundamental diagram, containing 3 traffic states: voids, capacity and jams. This fractal nature of traffic flow calls for analysis methods currently not used in our field.

scholarly journals On the set of Fixed Points of the Parallel Symmetric Sand Pile Model

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Kévin Perrot ◽  
Thi Ha Duong Phan ◽  
Trung Van Pham
Keyword(s):  
Fixed Points ◽  
Lexicographic Order ◽  
Sand Pile ◽  
Self Organized ◽  
Successor Relation ◽  
Self Organized Criticality ◽  
International Audience ◽  
Transition Rules ◽  
The Difference ◽  
Pile Model

International audience Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of $\textit{Self-Organized Criticality}$. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column if the difference of height between those columns is larger than 2. The model is nondeterministic and grains always fall downward. We propose a study of the set of fixed points reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Using a comparison with the Symmetric Sand Pile Model (SSPM) on which rules are applied once at each iteration, we get a continuity property. This property states that within PSSPM we can't reach every fixed points of SSPM, but a continuous subset according to the lexicographic order. Moreover we define a successor relation to browse exhaustively the sets of fixed points of those models.

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