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We propose that catastrophic events are "outliers" with statistically different properties than the rest of the population and result from mechanisms involving amplifying critical cascades. Applications and the potential for prediction are…
Statistical properties of the inhomogeneous version of the Olami-Feder-Christensen (OFC) model of earthquakes is investigated by numerical simulations. The spatial inhomogeneity is assumed to be dynamical. Critical features found in the…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
The Burridge-Knopoff model of earthquakes has recently gained increased interest for the consistency of the predicted energy released by sismic faults, with the Gutenberg-Richter scaling law. The present work suggests an improvement of this…
We show that the well established Olami-Feder-Christensen (OFC) model for the dynamics of earthquakes is able to reproduce a new striking property of real earthquake data. Recently, it has been pointed out by Abe and Suzuki that the…
The Gutenberg-Richter law is a fundamental empirical law in seismology describing earthquake frequency-magnitude distributions, with one of its key parameters, the so-called b-value, quantifying the relative frequency of small versus large…
The concept of memory is of central importance for characterizing complex systems and phenomena. Presence of long-term memories indicates how their dynamics can be less sensitive to initial conditions compared to the chaotic cases. On the…
A model for fault dynamics consisting of two rough and rigid brownian profiles that slide one over the other is introduced. An earthquake occurs when there is an intersection between the two profiles. The energy release is proportional to…
Ruptures of the largest earthquakes can last between a few seconds and several minutes. An early assessment of the final earthquake size is essential for early warning systems. However, it is still unclear when in the rupture history this…
Using long-term computer simulations and mean-field like arguments, we investigate the transient time and the properties of the stationary state of the Olami-Feder-Christensen earthquake model as function of the coupling parameter $\alpha$…
Many complex systems, including sand-pile models, slider-block models, and earthquakes, have been discussed whether they obey the principles of self-organized criticality. Behavior of these systems can be investigated from two different…
We analyze regional earthquake energy statistics from the Southern California and Japan seismic catalogs and find scale-invariant energy distributions characterized by an exponent $\tau \simeq 1.67$. To quantify how closely scale-invariant…
A multicomponent random process used as a model for the problem of space-time earthquake prediction; this allows us to develop consistent estimation for conditional probabilities of large earthquakes if the values of the predictor…
We study the predictability of large events in self-organizing systems. We focus on a set of models which have been studied as analogs of earthquake faults and fault systems, and apply methods based on techniques which are of current…
A statistical model for describing the scaling of the distribution of inter-event times is described. By considering the diverse region seismicity (natural and induced) at different scale levels the self-similarity of the distribution has…
We investigate numerically the Self Organized Criticality (SOC) properties of the dissipative Olami-Feder-Christensen model on small-world and scale-free networks. We find that the small-world OFC model exhibits self-organized criticality.…
We derive the exact equations of motion for the random neighbor version of the Olami-Feder-Christensen earthquake model in the infinite-size limit. We solve them numerically, and compare with simulations of the model for large numbers of…
Predicting extreme events in chaotic systems, characterized by rare but intensely fluctuating properties, is of great importance due to their impact on the performance and reliability of a wide range of systems. Some examples include…
The generalized logistic equation is derived to model kinetics and statistics of natural processes such as earthquakes, forest fires, floods, landslides, and many others. The general solution of this equation for q=1 is a product of an…
The upper bound earthquake magnitude (maximum possible magnitude) of a truncated Gutenberg-Richter relation is the right truncation point (right end-point) of a truncated exponential distribution and is important in the probabilistic…