1/F(ALPHA) Noise from Correlations Between Avalanches in Self-Organized Criticality (original) (raw)

Building blocks of self-organized criticality, part II: transition from very low drive to high drive

We analyze the transition of the self-organized criticality one dimensional directed running sandpile model of Hwa and Kardar [Phys. Rev. A 45, 7002 (1992)] from very low external forcing to high forcing, showing how six distinct power law regions in the power spectrum at low drive become four regions at high drive. One of these regions is due to long time correlations among events in the system and scales as ∼ f −β with 0 < β ≤ 1. The location in frequency space and the value of β both increase as the external forcing increases. β ranges from ≈ 0.4 for the weakest forcing studied here to a maximum value of 1 (i.e., a 1/f region) at stronger levels. The greatest rate of change in β is when the average quiet time between avalanche events is on the same order as the average duration of events. The correlations are quantified by a constant Hurst exponent H ≈ 0.8 when estimated by R/S analysis for sandpile driving rates spanning over five orders of magnitude. The constant H and changing β in the same system as forcing changes suggests that the power spectrum does not consistently quantify long time dynamical correlations and that the relation β = 2H − 1 does not hold for the time series produced by this SOC model. Because of the constant rules of the model we show that the same physics that produces a β = 1 scaling region during strong forcing produces a 0 < β < 1 region at weaker forcing.

Similarity of fluctuations in systems exhibiting Self-Organized Criticality

EPL (Europhysics Letters), 2011

PACS 89.75.Da -Systems obeying scaling laws PACS 95.75.Wx -Time series analysis, time variability PACS 91.30.Ab -Theory and modeling, computational seismology Abstract -The time-series of avalanches in three systems exhibiting SOC are analyzed in natural time χ. In two of them, i.e., ricepiles and magnetic flux penetration in thin films of YBa2Cu3O7−x, the data come from laboratory measurements, while the third one is a deterministic model mimicking stick-slip phenomena. We show that their scaled distributions for the variance κ1 of natural time exhibit an exponential tail as previously found for the order parameter in seismicity and in other non-equilibrium or equilibrium critical systems. Upon considering the entropy S− in natural time under time reversal, the following important difference is found: In ricepiles evolving to the critical state, S− is systematically larger than the entropy S in natural time, while in YBa2Cu3O7−x no systematic difference between S− and S is found.

Avalanches in Out of Equilibrium Systems: Statistical Analysis of Experiments and Simulations

2015

Instead of a linear and smooth evolution, many physical system react to external stimuli in avalanche dynamics. When an out of equilibrium system governed by disorder is externally driven the evolution of internal variables is local and non-homogeneous. This process is a collective behaviour adiabatically quick known as avalanches. Avalanche dynamics are associated to the transformation of spatial domains in different scales: from microscopic, to large catastrophic events such as earthquakes or solar flares. Avalanche dynamics is also involved in interdisiplinar topics such as the return prices of stock markets, the signalling in neuron networks or the biological evolution. Many avalanche dynamics are characterised by scale invariance, trademark of criticality. The physics in a so-called critical point are the same in all observational scales. Some avalanche dynamics share empirical laws and can define Universality Classes, reducing the complexity of systems to simpler mathematical ...

Avalanches, scaling, and coherent noise

Physical Review E, 1996

We present a simple model of a dynamical system driven by externally imposed coherent noise. Although the system never becomes critical in the sense of possessing spatial correlations of arbitrarily long range, it does organize into a stationary state characterized by avalanches with a power-law size distribution. We explain the behavior of the model within a time-averaged approximation, and discuss

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

Scientific Reports, 2019

In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. Here we make a linear stability analysis of the mean field fixed points of two self-organized quasi-critical systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism interrupts the oscillations, producing both power l...

Turbulent self-organized criticality

Physica A: Statistical Mechanics and its Applications, 2002

In the prototype sandpile model of self-organized criticality time series obtained by decomposing avalanches into waves of toppling show intermittent fluctuations. The q-th moments of wave size differences possess local multiscaling and global simple scaling regimes analogous to those holding for velocity structure functions in fluid turbulence. The correspondence involves identity of a basic scaling relation and of the form of relevant probability distributions. The sandpile provides a qualitative analog of many features of turbulent phenomena.

Finite-size scaling of critical avalanches

Physical Review E

We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it may decrease on increasing the system size at a fixed avalanche size. We implement the scaling method and identify scaling functions. The data collapse ensures a correct estimation of the critical exponents and distinguishes two exponents related to avalanche size and system size. Our simple analysis provides striking implications. While the exact value for avalanches size exponent remains elusive for the prototype sandpile on a square lattice, we suggest the exponent should be 1. The simulation results represent that the distribution shows a logarithmic system size dependence, consistent with the normalization condition. We also argue that for train or Oslo sandpile model with bulk drive, the avalanche size exponent is slightly less than 1 that is significantly different from the previous estimate 1.11.

Stochastic oscillations produce dragon king avalanches in self-organized quasi-critical systems

arXiv: Adaptation and Self-Organizing Systems, 2018

In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. This phenomenology has been called self-organized quasi-criticality (SOqC). Here we make a linear stability analysis of the mean field fixed points of two SOqC systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism ...