Evidence For Self-organized Criticality Research Articles

Evidence of self-organized criticality in time series by the horizontal visibility graph approach

Determination of self-organized criticality (SOC) is crucial in evaluating the dynamical behavior of a time series. Here, we apply the complex network approach to assess the SOC characteristics in synthesis and real-world data sets. For this purpose, we employ the horizontal visibility graph (HVG) method and construct the relevant networks for two numerical avalanche-based samples (i.e., sand-pile models), several financial markets, and a solar nano-flare emission model. These series are shown to have long-temporal correlations via the detrended fluctuation analysis. We compute the degree distribution, maximum eigenvalue, and average clustering coefficient of the constructed HVGs and compare them with the values obtained for random and chaotic processes. The results manifest a perceptible deviation between these parameters in random and SOC time series. We conclude that the mentioned HVG’s features can distinguish between SOC and random systems.

Ecological and Coevolutionary Dynamics in Modern Markets Yield Nonstationarity in Market Efficiencies

The U.S. stock market is one of the largest and most complex marketplaces in the global financial system. Over the past several decades, this market has evolved at multiple structural and temporal scales. New exchanges became active, and others stopped trading, regulations have been introduced and adapted, and technological innovations have pushed the pace of trading activity to blistering speeds. These developments have supported the growth of a rich machine‐trading ecology that leads to qualitative differences in trading behavior at human and machine time scales. We conduct a longitudinal analysis of comprehensive market data to quantify nonstationary dynamics throughout this system. We quantify the relationship between fluctuations in the number of active trading venues and realized opportunity costs experienced by market participants. We find that information asymmetries, in the form of quote dislocations, predict market‐wide volatility indicators. Lastly, we uncover multiple micro‐to‐macro level pathways, including those exhibiting evidence of self‐organized criticality.

Evidence for self-organized criticality in unscheduled downtime data of equipment

How to reduce downtime and improve availability of the complex equipment is very important. Although the unscheduled downtime(USDT) issues of the equipment are very complex, the self-organized criticality(SOC) is the right theory to study complex systems evolution and opens up a new window to the investigation of disasters, such as the sudden failure of the equipment. Firstly,SOC theory and its validation method are introduced. Then an SOC validation method for USDT of the equipment is proposed based on the above theory. Case study is done on bottleneck equipment in a factory and corresponding data pre-process work is done. The rescaled-range(R/S) analysis method is used to calculate the Hurst exponent of USDT time-series data in order to determine the long-range correlation of USDT data on time scale;at the same time the spatial power-law characteristic of USDT time series data is studied. The result shows that the characteristics of SOC are revealed in USDT data of the equipment according to the criterion of SOC. In addition, based on the characteristics of SOC,the overall framework of the prediction method for major sudden failure of the equipment is proposed based on SOC.

Avalanche duration time in a simple heterogeneous Olami–Feder–Christensen model

A modified version of the Olami–Feder–Christensen model has been introduced to consider the difference between avalanche duration distribution. The duration time of our model well demonstrates the power-law behavior and finite size scaling. Relationship between earthquake duration time and average size has been discussed. It gives a power-law behavior and provides a new evidence of self-organized criticality. We have investigated foreshock and aftershock and discovered that the probability of middle-size earthquake in the aftershock was significantly greater than others. The real data of Sichuan earthquake is in alignment with our model.

Analytical investigation of self-organized criticality in neural networks

Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity-dependent synaptic plasticity. Here, we model neurons as discrete-state nodes on an adaptive network following stochastic dynamics. At a threshold connectivity, this system undergoes a dynamical phase transition at which persistent activity sets in. In a low-dimensional representation of the macroscopic dynamics, this corresponds to a transcritical bifurcation. We show analytically that adding activity-dependent rewiring rules, inspired by homeostatic plasticity, leads to the emergence of an attractive steady state at criticality and present numerical evidence for the system's evolution to such a state.

Self-Organized Criticality of Rainfall in Central China

Rainfall is a complexity dynamics process. In this paper, our objective is to find the evidence of self-organized criticality (SOC) for rain datasets in China by employing the theory and method of SOC. For this reason, we analyzed the long-term rain records of five meteorological stations in Henan, a central province of China. Three concepts, that is, rain duration, drought duration, accumulated rain amount, are proposed to characterize these rain events processes. We investigate their dynamics property by using scale invariant and found that the long-term rain processes in central China indeed exhibit the feature of self-organized criticality. The proposed theory and method may be suitable to analyze other datasets from different climate zones in China.

Time series analysis of monthly rainfall in Nigeria with emphasis on self-organized criticality

Monthly rainfall data of twenty-one years (1980 – 2000) were analyzed for the six regions of Nigeria using the rescaled range (R/S) statistic, the standard fluctuation analysis (FA) and the detrended fluctuation analysis (DFA). The results indicated that the distribution of monthly rainfall has a Hurst exponent of 1 in the short term which is an evidence of self-organized criticality, and a Hurst exponent of about 0.5 in the long run which is an evidence of a random walk. The Hurst exponents decreased from around 1 for small window sizes and reached 0.5 after 36 months and then remained fairly constant. The R/S statistic was found to perform better than the FA and the linear DFA used in the analysis.

Evidence for Self-Organized Criticality in a Time Series of Electric Power System Blackouts

We analyze a 15-year time series of North American electric power transmission system blackouts for evidence of self-organized criticality (SOC). The probability distribution functions of various measures of blackout size have a power tail and rescaled range analysis of the time series shows moderate long-time correlations. Moreover, the same analysis applied to a time series from a sandpile model known to be self-organized critical gives results of the same form. Thus, the blackout data seem consistent with SOC. A qualitative explanation of the complex dynamics observed in electric power system blackouts is suggested.

Evidence for self-organized criticality in human epileptic hippocampus.

Self-organized criticality (SOC) is a property of complex dynamic systems that evolve to a critical state, capable of producing scale-free energy fluctuations. A characteristic feature of dynamical systems exhibiting SOC is the power-law probability distributions that describe the dynamics of energy release. We show experimental evidence for SOC in the epileptic focus of seven patients with medication-resistant temporal lobe epilepsy. In the epileptic focus the probability density of pathological energy fluctuations and the time between these energy fluctuations scale as (energy) and (time), respectively. The power-laws characterizing the probability distributions from these patients are consistent with computer simulations of integrate-and-fire oscillator networks that have been reported recently. These findings provide insight into the neuronal dynamics of epileptic hippocampus and suggest a mechanism for interictal epileptiform fluctuations. The presence of SOC in human epileptic hippocampus may provide a method for identifying the network involved in seizure generation.

Stylistic change as a self-organized critical phenomenon: An archaeological study in complexity

Archaeologists can learn from models of evolution as a self-organized critical phenomenon. Self-organized critical systems are large, interactive systems that organize into a critical state where minor events can trigger chain reactions. Such systems demonstrate power-law distributions in the size of changes, or “avalanches,” that occur. The theory of self-organized criticality is important in that it implies that the evolution of complex systems may be driven more by interactions between agents than by external events or natural selection. Stylistic changes may be examples of avalanches of interconnected events. Evidence for self-organized criticality is shown for stylistic evolution in historical pottery styles from New York State and is used to evaluate the nature of a prehistoric pottery typology from the Southwest.

Statistical Properties of SGR 1900+14 Bursts.

We study the statistics of soft gamma repeater (SGR) bursts using a database of 187 events detected with BATSE and 837 events detected with the Rossi X-Ray Timing Explorer Proportional Counter Array; all events are from SGR 1900+14 during its 1998-1999 active phase. We find that the fluence or energy distribution of bursts is consistent with a power law of index 1.66, over 4 orders of magnitude. This scale-free distribution resembles the Gutenberg-Richter law for earthquakes and gives evidence for self-organized criticality in SGRs. The distribution of time intervals between successive bursts from SGR 1900+14 is consistent with a lognormal distribution. There is no correlation between burst intensity and the waiting times till the next burst, but there is some evidence for a correlation between burst intensity and the time elapsed since the previous burst. We also find a correlation between the duration and the energy of the bursts, but with significant scatter. In all these statistical properties, SGR bursts resemble earthquakes and solar flares more closely than they resemble any known accretion-powered or nuclear-powered phenomena. Thus, our analysis lends support to the hypothesis that the energy source for SGR bursts is internal to the neutron star and plausibly magnetic.

Self-organized criticality in 1D stochastic traffic flow model with a speed limit

The aim of the present work is to investigate the effect of a speed limit 1 ≤ v max < ∞ on the phase diagram of the model with v max = ∞ considered in [1], as well as on the features of self-organized criticality (SOC) which have been observed there. Results of computer simulations and mean-field calculations of a 1D particle hopping model of traffic flow with a speed limit and open boundary conditions are presented here. The results are compared with the corresponding ones for the model without a speed limit. Evidence for SOC is found both in space and in time.

Evidence for self-organized criticality in the Bean critical state in superconductors

The time dependence of the magnetization of a type-II superconductor in the Bean critical state is studied. It is found that evolution occurs in the form of bursts, consistent with a model exhibiting self-organized criticality. The distribution of step sizes follows a power law with an exponent of a. 2. At high temperatures the distribution is Gaussian-like, as would be expected in an equilibrium situation. This may allow the experimental study of the occurrence of criticality. @S1063-651X~98!03508-9#

Self-organized criticality in 1D stochastic traffic flow model

Results of computer simulations of a 1D particle hopping model of traffic flow are presented. The model is characterized by parallel update and fully asymmetric stochastic hopping dynamics which allows unbounded series of jumps to empty neighbour sites on the right. The considered case of open boundary conditions can be used to model a “bottleneck” situation in traffic. Evidence for self-organized criticality is found in two aspects: the presence of long-range spatial correlations manifested in the shape of density profiles, and long-time temporal correlations showing up in the low-frequency behaviour of the spectral density of the total particle number and flow. A plausible conjecture is to interpret the observed qualitative changes in these features, as a function of the injection rate and the hopping probability, in terms of a nonequilibrium phase transition between a low-density phase and a maximal current phase. This conjecture is supported by the phase diagram obtained in mean-field approximation.

Evidence for self-organized criticality in evolution

Data of a number of different types have been put forward as evidence for self-organized critical behavior in evolution. These include fossil data on extinction rates and taxon lifetimes, evidence of fractal structure in taxonomic trees, and simulation data from experiments on artificial life. Here we present a new and very simple model of species origination and extinction which, although not critical, reproduces all of these data well. We suggest therefore, that data of these kinds should not be taken as evidence of self-organized criticality.

Evidence of self-organized criticality in insect populations

Self-organized criticality (SOC) occurs in systems consisting of a substrate or medium which can be locally stressed to a critical state. When the critical threshold is exceeded, the stress is distributed to the neighborhood around the locale, which can lead to critical states in the neighboring locations thereby propagating the disturbance. The SOC system manifests its behavior in distinctive temporal and spatial relationships. Diagnostic behaviors include conformity of dynamics to a power law (F(s) = βsα) relating the frequency distribution function to the observed behavior (1/f noise) and fractal behavior or spatial self-similarity. We analyzed 40 to 50 years of grasshopper infestations in Idaho and Montana for evidence of SOC. In both states, grasshopper infestations in four of the seven ecoregions statistically fit (the expected frequencies matched the observed with a probability of >95%) the power law relationship. In ecoregions where the model failed to fit the observed behavior, grasshopper infestations were typically rare and small scale. Spatial self-similarity was evident from graphical and statistical analyses. In both states there were statistically significant levels of concordance (among ranks) and correlation (among areas of infestations) between ecoregions. The spatial distributions of grasshopper infestations over time also showed considerable overlaps between ecoregions. However, only in Idaho were the variances in grasshopper infestations among ecoregions homogeneous. If rangeland grasshopper populations are SOC systems, then the management of outbreaks may need to be dramatically restructured. This system appears to be an example of “complex complexity,” in which multiple dynamics (i.e., the appearance of SOC with partial blockage of outbreaks, catastrophic dynamics, and perhaps chaos) give rise to a rich set of behaviors which arise at different scales and certainly necessitate further theoretical developments in order to understand. © 1997 John Wiley & Sons, Inc.

The Introduced Hawaiian Avifauna Reconsidered: Evidence for Self-Organized Criticality?

Over the last century, many bird species have been introduced into the Hawaiian islands. The data indicate a scenario in which island communities build up to a critical number of species, above which avalanches of extinction occur. Plotting the distribution of extinction event sizes approximates a power-law in accordance with the notion of a self-organized critical system. The lengths of time between introduction and extinction for different species also exhibit power-law scaling. These results suggest that ecological communities are not characterized by a well defined equilibrium, but rather by a detailed balance which is minimally stable to perturbations such that the introduction of species can trigger extinction cascades.

Experimental evidence of self organized criticality in the stick-slip dynamics of two rough elastic surfaces

An expenment on the stick slip dynamics of two elastic rough surfaces is de- scnbed. This dynamics produces a self organized cntical state on a wide range of control parameters, namely loading speed and pressure. The dependence on the system size has also been studied. A comparison with the stick-slip dynamics produced by a one d1nlensional system and by two rigid surfaces is made.

Frequency distributions of solar X-ray flare parameters

We have determined frequency distributions of flare parameters from the over 12,000 solar flares that were recorded with the Hard X-ray Burst Spectrometer (HXRBS) on SMM. These parameters include the total flare duration, peak counting rate, the peak hard X-ray flux, the total energy in electrons, and the peak hard X-ray flux in electrons (the latter two computed assuming a thick-target model). The energies were computed above a threshold energy between 25 and 50 keV. All the distributions can be represented by power-laws over a range of several orders of magnitude, above the HXRBS sensitivity threshold. Power-laws can be taken as evidence for self-organized criticality in solar flares. Correlations among these parameters are determined from linear regression fits as well as from the slopes from the frequency distributions. Variations of the frequency distributions were also investigated with respect to the solar cycle.

Effect of flux avalanches on activation energy in type-II superconductors: Evidence for self-organized criticality.

The behavior of thermally activated flux avalanches is studied for both high-${\mathit{T}}_{\mathit{c}}$ superconductors (single crystals of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{\mathit{x}}$ and ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$) and a conventional type-II superconductor (${\mathrm{Nb}}_{3}$Sn multifilamentary wire). By combining two different mechanisms, namely, thermally activated and avalanche flux motion, we have developed a U(j) relationship in a large regime of driving force for type-II superconductors. As a result of flux avalanches, the flux-motion activation energy is considerably reduced. We have found a dynamic crossover at which the flux-motion characteristic changes from spatially and temporally correlated flux avalanches to slow creep.