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In this letter we aim to describe the seismic activity of the Rigan earthquake 2010, using the virtual seismometer (ViS) technique. By defining avalanche-type dynamics on top of the ViS complex network, we show that the seismic activity is strongly intermittent, and is cyclic as seen in the natural situations. This model is based on avalanches during which signals, as a simulation of the real seismic signals, travel between regions that already were connected on the ViS network. This network is mainly characterized by a power-law distribution of the degree of nodes with an exponent γ = 2.3 ± 0.2. The branching ratio inside and between avalanches reveals that the system is in a critical state showing power-law behavior for the distribution function of the mass, the duration and the size of the avalanches, the critical exponent of the latter being τS = 1.45 ± 0.02. We find a considerable correlation between the dynamical Green function and the nodes centralities, showing that the simulated signals are close to the real seismic signals, from which we constructed the complex network.

Some features of random networks with excitable nodes that are embeddable in the Euclidean space are not describable in terms of the conventional integrate and fire model (IFM) alone, and some further details should be involved. In the present paper we consider the effect of the retardation, i.e. the time that is needed for a signal to traverse between two agents. This effect becomes important to discover the differences between e.g. the neural networks with low and fast axon conduct times. We show that the inclusion of the retardation effects makes some important changes in the statistical properties of the system. It considerably suppresses/restricts the amplitude of the possible oscillations in the random network. Additionally, it causes the critical exponents in the critical regime to considerably change.

This paper is devoted to a phenomenological study of the earthquakes in central Alborz, Iran. Using three observational quantities, namely weight function, quality factor, and velocity model in this region, we develop a phenomenological dissipative sandpile-like 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 are chosen (I) randomly, (II) on the faults, (III) on the highly active points in the region. We analyze all these cases and show some universal behaviors of the system depending slightly on the method of external stimuli. The multi-fractal analysis is exploited to extract the spectrum of the Hurst exponent of time series obtained by each of these schemes. Although the average Hurst exponent depends on the method of stimuli (the three cases mentioned above), we numerically show that in all cases it is lower than 0.5, reflecting the anticorrelated nature of the system. The lowest average Hurst exponent is for the case (III), in such a way that the more active the stimulated sites are the lower the value for the average Hurst exponent is obtained, i.e. the larger earthquakes are more anticorrelated. However, the different activity fields in this study provide the depth of the basement, the depth variation (topography) of the basement, and an area that can be the location of the future probability event.

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.

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).

The analysis of the dynamics of a large class of excitable systems on locally tree-like networks leads to the conclusion that at λ = 1 a continuous phase transition takes place, where λ is the largest eigenvalue of the adjacency matrix of the network. This paper is devoted to evaluate this claim for a more general case where the assumption of the linearity of the dynamical transfer function is violated with a non-linearity parameter β which interpolates between stochastic (β = 0) and deterministic (β → ∞) dynamics. Our model shows a rich phase diagram with an absorbing state and extended critical and oscillatory regimes separated by transition and bifurcation lines which depend on the initial state. We test initial states with (I) only one initial excited node, (II) a fixed fraction (10%) of excited nodes, for all of which the transition is of first order for β > 0 with a hysteresis effect and a gap function. For the case (I) in the thermodynamic limit the absorbing state in the only phase for all λ values and β > 0. We further develop mean-field theories for cases (I) and (II). For case (II) we obtain an analytic one-dimensional map which explains the essential properties of the model, including the hysteresis diagrams and fixed points of the dynamics.