scholarly journals A stochastic theory for temporal fluctuations in self-organized critical systems

2008 ◽  
Vol 10 (12) ◽  
pp. 123010 ◽  
Author(s):  
M Rypdal ◽  
K Rypdal
Keyword(s):  
Stochastic Theory ◽  
Critical Systems ◽  
Temporal Fluctuations ◽  
Self Organized

scholarly journals Persistent dynamic correlations in self-organized critical systems away from their critical point

2007 ◽  
Vol 373 ◽  
pp. 215-230 ◽  
Author(s):  
Ryan Woodard ◽  
David E. Newman ◽  
Raúl Sánchez ◽  
Benjamin A. Carreras
Keyword(s):  
Critical Point ◽  
Critical Systems ◽  
Dynamic Correlations ◽  
Self Organized

scholarly journals THE SELF-ORGANIZED MULTI-LATTICE MONTE CARLO SIMULATION

2004 ◽  
Vol 15 (09) ◽  
pp. 1249-1268 ◽  
Author(s):  
DENIS HORVÁTH ◽  
MARTIN GMITRA
Keyword(s):  
Monte Carlo ◽  
Finite Size ◽  
Simulation Method ◽  
Monte Carlo Step ◽  
The Self ◽  
Square Lattice ◽  
Critical Systems ◽  
Lattice Systems ◽  
Steady Regime ◽  
Self Organized

Self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of the suggested simulation method is an artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by a random walk on the temperature axis. The walk is biased towards the critical region through a feedback based on instantaneous energy and magnetization cumulants, which are updated at every Monte Carlo step and filtered through a special recursion algorithm. The simulations revealed the invariance of the temperature probability distribution function, once some self-organized critical steady regime is reached, which is called here noncanonical equilibrium. The mean value of this distribution approximates the pseudocritical temperature of canonical equilibrium. In order to suppress finite-size effects, the self-organized approach is extended to multi-lattice systems, where the feedback basis on pairs of instantaneous estimates of the fourth-order magnetization cumulant on two systems of different size. These replica-based simulations resemble, in Monte Carlo lattice systems, some of the invariant statistical distributions of standard self-organized critical systems.

scholarly journals Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Osame Kinouchi ◽  
Ludmila Brochini ◽  
Ariadne A. Costa ◽  
João Guilherme Ferreira Campos ◽  
Mauro Copelli
Keyword(s):  
Critical Systems ◽  
Self Organized ◽  
Stochastic Oscillations

scholarly journals Some properties of sandpile models as prototype of self-organized critical systems

2021 ◽  
Vol 96 (11) ◽  
pp. 112001
Author(s):  
M N Najafi ◽  
S Tizdast ◽  
J Cheraghalizadeh
Keyword(s):  
Critical Systems ◽  
Self Organized ◽  
Sandpile Models

TEMPORAL FLUCTUATIONS IN BIORHYTHMS: EXPRESSION OF SELF-ORGANIZED CRITICALITY?

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 380-387 ◽  
Author(s):  
KLAUS-D. KNIFFKI ◽  
WOLFGANG MANDEL ◽  
PHUOC TRAN-GIA
Keyword(s):  
Point Process ◽  
Critical State ◽  
Degrees Of Freedom ◽  
Low Frequency ◽  
Well Being ◽  
Scale Invariant ◽  
Low Frequencies ◽  
Temporal Fluctuations ◽  
Self Organized ◽  
The Individual

Recently, a general organizing principle has been reported connecting 1/f-noise with the self-similar scale-invariant ‘fractal’ properties in space, hence reflecting two sides of a coin, the so-called self-organized critical state. The basic idea is that dynamical systems with many degrees of freedom operate persistently far from equilibrium at or near a threshold of stability at the border of chaos. Temporal fluctuations which cannot be explained as consequences of statistically independent random events are found in a variety of physical and biological phenomena. The fluctuations of these systems can be characterized by a power spectrum density S(f) decaying as f−b at low frequencies with an exponent b<1.5. We present a new approach to describe the individual biorhythm of humans using data from a colleague who has kept daily records for two years of his state of well-being applying a fifty-point magnitude category scale. This time series was described as a point process by introducing two discriminating rating levels R for the occurrence of R≥40 and R≤10. For b<1 a new method to estimate the low frequency part of S(f) was applied using counting statistics without applying Fast Fourier Transform. The method applied reliably discriminates these types of fluctuations from a random point process, with b=0.0. It is very tempting to speculate that the neural mechanisms at various levels of the nervous system underlying the perception of different values of the subjective state of well-being, are expressions of a self-organized critical state.

scholarly journals The emergence of integrated information, complexity, and consciousness at criticality

2019 ◽  
Author(s):  
Sina Khajehabdollahi ◽  
Pubuditha M. Abeyasinghe ◽  
Adrian M. Owen ◽  
Andrea Soddu
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Critical Point ◽  
Critical Systems ◽  
Dynamical Phase ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Ancient Problem ◽  
Emergence Of Complexity ◽  
Integrated Information

AbstractUsing the critical Ising model of the brain, integrated information as a measure of consciousness is measured in toy models of generic neural networks. Monte Carlo simulations are run on 159 random weighted networks analogous to small 5-node neural network motifs. The integrated information generated by this sample of small Ising models is measured across the model parameter space. It is observed that integrated information, as a type of order parameter not unlike a concept like magnetism, undergoes a phase transition at the critical point in the model. This critical point is demarcated by the peaks of the generalized susceptibility of integrated information, a point where the ‘consciousness’ of the system is maximally susceptible to perturbations and on the boundary between an ordered and disordered form. This study adds further evidence to support that the emergence of consciousness coincides with the more universal patterns of self-organized criticality, evolution, the emergence of complexity, and the integration of complex systems.Author summaryUnderstanding consciousness through a scientific and mathematical language is slowly coming into reach and so testing and grounding these emerging ideas onto empirical observations and known systems is a first step to properly framing this ancient problem. This paper in particular explores the Integrated Information Theory of Consciousness framed within the physics of the Ising model to understand how and when consciousness, or integrated information, can arise in simple dynamical systems. The emergence of consciousness is treated like the emergence of other classical macroscopic observables in physics such as magnetism and understood as a dynamical phase of matter. Our findings show that the sensitivity of consciousness in a complex system is maximized when the system is undergoing a phase transition, also known as a critical point. This result, combined with a body of evidence highlighting the privelaged state of critical systems suggests that, like many other complex phenomenon, consciousness may simply follow from/emerge out of the tendency of a system to self-organize to criticality.

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