Nebojša Vasović

Activation process in excitable systems with multiple noise sources: One and two interacting units.

We consider the coaction of two distinct noise sources on the activation process of a single excitable unit and two interacting excitable units, which are mathematically described by the Fitzhugh-Nagumo equations. We determine the most probable activation paths around which the corresponding stochastic trajectories are clustered. The key point lies in introducing appropriate boundary conditions that are relevant for a class II excitable unit, which can be immediately generalized also to scenarios involving two coupled units. We analyze the effects of the two noise sources on the statistical features of the activation process, in particular demonstrating how these are modified due to the linear or nonlinear form of interactions. Universal properties of the activation process are qualitatively discussed in the light of a stochastic bifurcation that underlies the transition from a stochastically stable fixed point to continuous oscillations.

Spontaneous formation of synchronization clusters in homogenous neuronal ensembles induced by noise and interaction delays.

The spontaneous formation of clusters of synchronized spiking in a structureless ensemble of equal stochastically perturbed excitable neurons with delayed coupling is demonstrated for the first time. The effect is a consequence of a subtle interplay between interaction delays, noise, and the excitable character of a single neuron. The dependence of the cluster properties on the time lag, noise intensity, and the synaptic strength is investigated.

Triggered dynamics in a model of different fault creep regimes.

The study is focused on the effect of transient external force induced by a passing seismic wave on fault motion in different creep regimes. Displacement along the fault is represented by the movement of a spring-block model, whereby the uniform and oscillatory motion correspond to the fault dynamics in post-seismic and inter-seismic creep regime, respectively. The effect of the external force is introduced as a change of block acceleration in the form of a sine wave scaled by an exponential pulse. Model dynamics is examined for variable parameters of the induced acceleration changes in reference to periodic oscillations of the unperturbed system above the supercritical Hopf bifurcation curve. The analysis indicates the occurrence of weak irregular oscillations if external force acts in the post-seismic creep regime. When fault motion is exposed to external force in the inter-seismic creep regime, one finds the transition to quasiperiodic- or chaos-like motion, which we attribute to the precursory creep regime and seismic motion, respectively. If the triggered acceleration changes are of longer duration, a reverse transition from inter-seismic to post-seismic creep regime is detected on a larger time scale.

Mean-field approximation of two coupled populations of excitable units.

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of N stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the interensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset, and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical interpopulation couplings.

A new approach to grid search method in slope stability analysis using Box-Behnken statistical design

Prediction model for safety factor is developed using statistical design.Explicit equations for locating the slip center grid are proposed.Impact of geometrical and soil parameters on slope stability is thoroughly evaluated. Grid search method for locating the critical failure surface is extended by deriving additional analytical expressions for slip center grid (xmin, zmin; xmax, zmax), where global minimum of safety factor occurs, including the prediction of minimum and maximum values for safety factor (Fsmin,max) and for slip circle radius (Rmin,max). Derived models are proposed in a form of nonlinear functions of geometrical parameters (slope height H, depth to bedrock d and slope angle β) and soil factors (bulk density γ, cohesion c, angle of internal friction ? and pore water pressure coefficient ru). Research was performed using Box-Behnken experimental design, for which the input data were provided by Spencer limit equilibrium analyzes of different slopes with circular slip surface. Reasonable predictive power of the proposed models was verified both by internal and external validation, latter of which included the analyzes of slopes with random geometrical and soil properties. Regarding the impact of input parameters, β has the strongest influence on response values (Fs, R, x, z), with the predominant linear and quadratic effect. As for the influence of remaining factors, c and ? also have strong impact on Fs, while H and ? have significant influence on slip circle radius and the location of slip center grid. However, due to existence of two-factor interactions, it is shown that the effect of β on Fs, x, z and R is highly dependent on the values of c, ?, ru, H and d/H, including the significant effect of rui??, ci?H and ci?γ. When compared to traditional grid search method, proposed approach could be used to locate the circular slip surface with global minimum of safety factor, without the need for additional slope stability analyzes.

Predictions of Experimentally Observed Stochastic Ground Vibrations Induced by Blasting

In the present paper, we investigate the blast induced ground motion recorded at the limestone quarry “Suva Vrela” near Kosjerić, which is located in the western part of Serbia. We examine the recorded signals by means of surrogate data methods and a determinism test, in order to determine whether the recorded ground velocity is stochastic or deterministic in nature. Longitudinal, transversal and the vertical ground motion component are analyzed at three monitoring points that are located at different distances from the blasting source. The analysis reveals that the recordings belong to a class of stationary linear stochastic processes with Gaussian inputs, which could be distorted by a monotonic, instantaneous, time-independent nonlinear function. Low determinism factors obtained with the determinism test further confirm the stochastic nature of the recordings. Guided by the outcome of time series analysis, we propose an improved prediction model for the peak particle velocity based on a neural network. We show that, while conventional predictors fail to provide acceptable prediction accuracy, the neural network model with four main blast parameters as input, namely total charge, maximum charge per delay, distance from the blasting source to the measuring point, and hole depth, delivers significantly more accurate predictions that may be applicable on site. We also perform a sensitivity analysis, which reveals that the distance from the blasting source has the strongest influence on the final value of the peak particle velocity. This is in full agreement with previous observations and theory, thus additionally validating our methodology and main conclusions.

Mean field approximation for noisy delay coupled excitable neurons

Mean field approximation of a large collection of FitzHugh–Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by N≫1 stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.

Slope Stability Analysis Based on Experimental Design

AbstractIn this paper, the authors propose an analytical model for the prediction of the slope safety factor as a function of basic geometrical parameters (slope height H and slope angle β) and soil factors (bulk density γ, cohesion c, angle of internal friction φ, and pore water pressure coefficient ru). Research was performed by applying the statistical technique of experimental design, for which the input data were provided by stability analyses of different homogeneous slopes with a circular slip surface using the Spencer limit equilibrium method. The proposed model represents a nonlinear equation of a simpler form and higher prediction accuracy than those of the existing mathematical expressions, with predominant linear effect of the individual factors and significant influence of the two-factor interactions. Linear terms in a derived equation indicate a positive effect of c or φ and a negative effect of H, β, γ, or ru on slope stability. Because of two-factor interactions, the effect of c is highly ...

Stability of earth slopes under the effect of main environmental properties of weathered clay–marl deposits in Belgrade (Serbia)

In the present paper, the impact of the main environmental factors on slope stability is analyzed by deriving a model for slope safety factor as a nonlinear function of geomechanical soil properties (bulk density γ, cohesion c, angle of internal friction φ and pore water pressure coefficient ru) and terrain geometry (slope height H, bedrock depth d and slope angle β). The suggested model is derived using the response surface method, based on Spencer’s stability analyses of homogeneous slopes with circular slip surface. The analyzed parameter ranges were chosen according to the commonly determined values for unstable slopes in Neogene clay–marl deposits in Belgrade. The statistical reliability of the suggested model was confirmed by analyzing the stability of slopes with random geomechanical soil properties and terrain geometry. The obtained results indicate that all the examined environmental factors have statistically significant impact on the slope stability with prevailing linear effect, while geometrical factors and cohesion also show substantial quadratic effect. The existence of two-factor interactions imply that the impact of slope height on its stability is strongly dependent on slope angle, cohesion and bedrock depth, while the latter two also significantly affect the impact of slope angle on Fs.

Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units.

We consider the approximations behind the typical mean-field model derived for a class of systems made up of type II excitable units influenced by noise and coupling delays. The formulation of the two approximations, referred to as the Gaussian and the quasi-independence approximation, as well as the fashion in which their validity is verified, are adapted to reflect the essential properties of the underlying system. It is demonstrated that the failure of the mean-field model associated with the breakdown of the quasi-independence approximation can be predicted by the noise-induced bistability in the dynamics of the mean-field system. As for the Gaussian approximation, its violation is related to the increase of noise intensity, but the actual condition for failure can be cast in qualitative, rather than quantitative terms. We also discuss how the fulfillment of the mean-field approximations affects the statistics of the first return times for the local and global variables, further exploring the link between the fulfillment of the quasi-independence approximation and certain forms of synchronization between the individual units.