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

This paper is devoted to a phenomenological study of the earthquakes in central Alborz, Iran. Using three observational quantities, namely the weight function, the quality factor, and the velocity model in this region, we develop a modified dissipative sandpile model which captures the main features of the system, especially the average activity field over the region of study. The model is based on external stimuli, the location of which is chosen (I) randomly, (II) on the faults, (III) on the low active points, (IV) on the moderately active points, and (V) on the highly active points in the region. We uncover some universal behaviors depending slightly on the method of external stimuli. A multi-fractal detrended fluctuation analysis is exploited to extract the spectrum of the Hurst exponent of the time series obtained by each of these schemes. Although the average Hurst exponent depends slightly on the method of stimuli, we numerically show that in all cases it is lower than 0.5, reflecting the anti-correlated nature of the system. The lowest average Hurst exponent is found to be associated with the case (V), in such a way that the more active the stimulated sites are, the lower the average Hurst exponent is obtained, i.e. the large earthquakes are more anticorrelated. Moreover, we find that the activity field achieved in this study provide information about the depth and topography of the basement, and also the area that can potentially be the location of the future large events. We successfully determine a high activity zone on the Mosha Fault, where the mainshock occurred on May 7th, 2020 (M$$_W$$ W 4.9).

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Stochastic and deterministic dynamics in networks with excitable nodes

Rahimi-Majd

Restrepo

Najafi

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Networks of excitable systems provide a flexible and tractable model for various phenomena in biology, social sciences, and physics. A large class of such models undergo a continuous phase transition as the excitability of the nodes is increased. However, models of excitability that result in this continuous phase transition are based implicitly on the assumption that the probability that a node gets excited, its transfer function, is linear for small inputs. In this paper, we consider the effect of cooperative excitations, and more generally the case of a nonlinear transfer function, on the collective dynamics of networks of excitable systems. We find that the introduction of any amount of nonlinearity changes qualitatively the dynamical properties of the system, inducing a discontinuous phase transition and hysteresis. We develop a mean-field theory that allows us to understand the features of the dynamics with a one-dimensional map. We also study theoretically and numerically finite-size effects by examining the fate of initial conditions where only one node is excited in large but finite networks. Our results show that nonlinear transfer functions result in a rich effective phase diagram for finite networks, and that one should be careful when interpreting predictions of models that assume noncooperative excitations.

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

Cited by 6 publications

References 204 publications

Pseudo Random Number Generator Based on Cellular Automata with Self Organized Criticality

Pseudo Random Number Generator Based on Cellular Automata with Self Organized Criticality

A self-organized critical model and multifractal analysis for earthquakes in Central Alborz, Iran

Stochastic and deterministic dynamics in networks with excitable nodes

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