"SPIRAL WAVE–TRAVELING CLUSTERING" INTERMITTENCY AND 1/f-NOISE IN A 2D COUPLED MAP LATTICE

1999 ◽  
Vol 09 (05) ◽  
pp. 929-937 ◽  
Author(s):  
MARK A. PUSTOVOIT ◽  
VALERY I. SBITNEV
Keyword(s):  
Probability Density ◽  
Exponential Decay ◽  
Power Law ◽  
Strange Attractor ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
The Self ◽  
Saddle Node Bifurcation ◽  
Self Organized

Intermittency of checkerboard spiral waves and traveling clusterings originating from sudden shrinking of the strange attractor of the 2D CML in the neighborhood of the saddle-node bifurcation boundary is found. A power-law probability density for lifetimes in the spiral wave (laminar) phase is observed, while in the checkerboard clusterings (bursting) phase the above quantity exhibits an exponential decay. This difference can be interpreted through the self-organized behavior of the spiral waves, and the passive relaxation of the disordered checkerboard clusterings.

CHECKERBOARD SPIRAL WAVES IN A 2D COUPLED MAP LATTICE: SCALING EVIDENCE

1999 ◽  
Vol 09 (05) ◽  
pp. 919-928 ◽  
Author(s):  
VALERY I. SBITNEV ◽  
ALEX. O. DUDKIN
Keyword(s):  
Close Agreement ◽  
Diffusion Length ◽  
Spiral Wave ◽  
Spatiotemporal Chaos ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
Self Organization ◽  
Natural Unit ◽  
Saddle Node Bifurcation ◽  
Unit Of Length

Checkerboard spiral waves in a 2D CML under consideration are generic solutions in a narrow parameter layer located adjacent to the saddle-node bifurcation boundary in the spatiotemporal chaos region. The spiral wave self-organization is in close agreement with the Haken's slaving principle. Scaling correspondence between sizes of the spiral waves and the diffusion length that is a natural unit of length in the CML is established.

scholarly journals Extra investigation of the self-organized critical Manna model at higher critical dimension

2021 ◽  
pp. 1-12
Author(s):  
Andrey Viktorovich Podlazov
Keyword(s):  
Power Law ◽  
Critical Dimension ◽  
The Self ◽  
Two Dimensional ◽  
Upper Critical Dimension ◽  
Self Organized ◽  
Logarithmic Corrections ◽  
Universal Indicator ◽  
Sandpile Models ◽  
Power Law Distributions

I investigate the nature of the upper critical dimension for isotropic conservative sandpile models and calculate the emerging logarithmic corrections to power-law distributions. I check the results experimentally using the case of Manna model with the theoretical solution known for all statement starting from the two-dimensional one. In addition, based on this solution, I construct a non-trivial super-universal indicator for this model. It characterizes the distribution of avalanches by time the border of their region needs to pass its width.

scholarly journals Predictability of spatio-temporal patterns in a lattice of coupled FitzHugh–Nagumo oscillators

2013 ◽  
Vol 10 (81) ◽  
pp. 20121016 ◽  
Author(s):  
Miriam Grace ◽  
Marc-Thorsten Hütt
Keyword(s):  
Dynamical System ◽  
Spiral Wave ◽  
Temporal Patterns ◽  
Spiral Waves ◽  
Generic Model ◽  
Homogeneous State ◽  
Drift Speed ◽  
Statistical Fluctuations ◽  
Self Organized ◽  
Spatio Temporal

In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. In pioneering work in the late 1990s, it was hypothesized that a drift of cellular parameters (along a ‘developmental path’), together with differences in cell properties (‘desynchronization’ of cells on the developmental path) can establish self-organized spatio-temporal patterns (in their example, spiral waves of cAMP in a colony of Dictyostelium discoideum cells) starting from a homogeneous state. Here, we embed a generic model of an excitable medium, a lattice of diffusively coupled FitzHugh–Nagumo oscillators, into a developmental-path framework. In this minimal model of spiral wave generation, we can now study the predictability of spatio-temporal patterns from cell properties as a function of desynchronization (or ‘spread’) of cells along the developmental path and the drift speed of cell properties on the path. As a function of drift speed and desynchronization, we observe systematically different routes towards fully established patterns, as well as strikingly different correlations between cell properties and pattern features. We show that the predictability of spatio-temporal patterns from cell properties contains important information on the pattern formation process as well as on the underlying dynamical system.

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).

Sandpiles

2017 ◽  
Author(s):  
Paul Charbonneau
Keyword(s):  
Power Law ◽  
Slope Angle ◽  
The Self ◽  
Numerical Implementation ◽  
Sandpile Model ◽  
Self Organized ◽  
Self Organized Criticality

This chapter describes a simple computational idealization of a sandpile. When sand trickles slowly through your fingers, a small conical pile of sand forms below your hand. Sand avalanches of various sizes intermittently slide down the slope of the pile, which is growing both in width and in height but maintains the same slope angle. The pile of sand is a classic example of self-organized criticality. The chapter first provides an overview of the sandpile model before discussing its numerical implementation and a representative simulation involving a small 100-node lattice. It then examines the invariant power-law behavior of avalanches and the self-organized criticality of a sandpile. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.

scholarly journals Multiobjective Optimization Of An Extremal Evolution Model

2005 ◽  
Vol 60 (5) ◽  
pp. 335-342 ◽  
Author(s):  
Mohamed Fathey Elettreby
Keyword(s):  
Multiobjective Optimization ◽  
Power Law ◽  
Lattice Model ◽  
Critical State ◽  
Coupled Map Lattice ◽  
Evolution Model ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Self Organized ◽  
Two Dimensional Model

We propose a two-dimensional model for a co-evolving ecosystem that generalizes the extremal coupled map lattice model. The model takes into account the concept of multiobjective optimization. We find that the system is self-organized into a critical state. The distribution of avalanche sizes follows a power law.

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 A Statistical Study of Flares as Self-Organized Critical Phenomena

1993 ◽  
Vol 141 ◽  
pp. 369-372
Author(s):  
Yoshinari Nakagawa
Keyword(s):  
Solar Activity ◽  
Solar Cycle ◽  
Critical Phenomena ◽  
Power Law ◽  
Statistical Study ◽  
Critical Phenomenon ◽  
The Self ◽  
Statistical Property ◽  
Self Organized

AbstractThe statistical property of flares is examined in terms of the number of flares versus its magnitude, i. e. the “Importance” reported in the IAU Quarterly Bulletin of Solar Activity for 1961–1983. It is shown that the number of flare and its magnitude follow a power law relationship indicative of the self-organized critical phenomenon, regardless of the phase of the solar cycle.

Chaos Structure and Spiral Wave Self-Organization in 2D Coupled Map Lattice

1998 ◽  
Vol 08 (12) ◽  
pp. 2341-2352 ◽  
Author(s):  
Valery I. Sbitnev
Keyword(s):  
Quantitative Analysis ◽  
Entropy Production ◽  
Statistical Physics ◽  
Nonequilibrium Thermodynamics ◽  
Spiral Wave ◽  
Spatiotemporal Chaos ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
Self Organization ◽  
Entropy Variation

Methods borrowed from nonequilibrium thermodynamics and statistical physics have been employed in the quantitative analysis of spatiotemporal chaos in a 2D coupled map lattice (CML). Emphasis is made on entropy, entropy variation and entropy production. These quantities manifest peculiar changes in a region where spiral waves emerge. The spiral waves observed in the 2D CML are found to be dissipative objects with an elevated entropy production.

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.

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