1. Transport and Localization in Classical and Quantum BilliardsČrt Lozej, 2020, doctoral dissertation Abstract: In this thesis the classical and quantum dynamics in billiard systems are considered. Extensive numerical studies of the classical transport properties in several examples of billiard families including the ergodic Bunimovich stadium and cutcircle billiards and the mixedtype Robnik and lemon billiards are performed. The analysis of the transport is based on the random model of diffusion which assumes that due the strongly chaotic dynamics the motion of the orbit on the discretized phase space is temporally uncorrelated. The cause of the deviations from the random model dynamics is traced to dynamical trapping due to stickiness. A novel approach to locally quantifying stickiness based on the statistics of the recurrence times is presented and applied to distinguish between exponential decays of recurrence times and other types of decays. This enables the identification of sticky areas in the chaotic components. Detailed maps of their structure for a wide range of parameter values, mapping the evolution of the mixedphase spaces and revealing some particularly interesting special examples are presented. The recurrence time distributions in sticky areas are found to be well described by a mixture of exponential decays. The transport of particle ensembles in the momentum space of classical billiards is described by using an inhomogeneous diffusion model and the classical transport times are determined. The classical transport times are vital for the analysis of the localization of chaotic eigenstates in quantum billiards. The control parameter that describes the the degree of localization of the chaotic quantum eigenstates is the ratio between the Heisenberg time (Planck's constant divided by the mean level spacing) and the classical transport time. Extensive numerical calculations of the highlying spectra and eigenstates of the stadium, Robnik and lemon quantum billiards are performed. The spectral statistics are analysed in terms of the standard methods of quantum chaos. The level repulsion exponent of localized eigenstates is found to be a rational function of the control parameter. The degree of localization is determined with respect to localization measures based on the PoincaréHusimi representation of the eigenstates. The mean localization measure is found to be a rational function of the control parameter and linearly related to the level repulsion exponent. The distributions of the localization measures are analysed and found to be of a universal shape well described by a two parameter empirical distribution in billiards with no apparent stickiness. The nonuniversal system specific features of localization measure distributions are related to the presence of sticky areas in the phase spaces of classical billiards with specific examples shown. Keywords: Transport, localization, chaos, quantum chaos, Hamiltonian systems, level spacing distribution, mixed phase space, billiard, quantum billiard, Husimi functions, stickiness, cantorus, chaotic eigenstates, level repulsion. Published: 13.01.2021; Views: 395; Downloads: 73 Full text (24,93 MB) 
2. Triggered dynamics in a model of different fault creep regimesSrđan Kostić, Igor Franović, Matjaž Perc, Nebojša Vasović, Kristina Todorović, 2014, original scientific article Abstract: 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 springblock model, whereby the uniform and oscillatory motion correspond to the fault dynamics in postseismic and interseismic 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 postseismic creep regime. When fault motion is exposed to external force in the interseismic creep regime, one finds the transition to quasiperiodic or chaoslike 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 interseismic to postseismic creep regime is detected on a larger time scale. Keywords: geophysics, nonlinear dynamics, chaos, earthquake Published: 23.06.2017; Views: 784; Downloads: 298 Full text (669,71 KB) This document has many files! More...

3. Predictions of experimentally observed stochastic ground vibrations induced by blastingSrđan Kostić, Matjaž Perc, Nebojša Vasović, Slobodan Trajković, 2013, original scientific article Abstract: 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, timeindependent 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. Keywords: blasting, vibrations, surrogate data, deterministic chaos, stochasticity Published: 19.06.2017; Views: 493; Downloads: 268 Full text (1,45 MB) This document has many files! More...

4. Particle swarm optimization for automatic creation of complex graphic charactersIztok Fister, Matjaž Perc, Karin Fister, Salahuddin M. Kamal, Andres Iglesias, Iztok Fister, 2015, original scientific article Abstract: Natureinspired algorithms are a very promising tool for solving the hardest problems in computer sciences and mathematics. These algorithms are typically inspired by the fascinating behavior at display in biological systems, such as bee swarms or fish schools. So far, these algorithms have been applied in many practical applications. In this paper, we present a simple particle swarm optimization, which allows automatic creation of complex twodimensional graphic characters. The method involves constructing the base characters, optimizing the modifications of the base characters with the particle swarm optimization algorithm, and finally generating the graphic characters from the solution. We demonstrate the effectiveness of our approach with the creation of simple snowman, but we also outline in detail how more complex characters can be created. Keywords: optimizacija roja, kompleksni sistem, kaos, particle swarm optimization, complex system, graphics, chaos Published: 07.04.2017; Views: 1001; Downloads: 78 Link to full text 
5. The periodicity of the anticipative discrete demandsupply modelAndrej Škraba, Davorin Kofjač, Črtomir Rozman, 2006, original scientific article Keywords: cobweb, hiperincursivity, system dynamics, anticipative system, nonlinear system, Farey tree, chaos Published: 10.07.2015; Views: 586; Downloads: 21 Link to full text 
6. Applying chaos theory to lesson planning and deliverySlavko Cvetek, 2007, published scientific conference contribution Keywords: vzgoja in izobraževanje, izobraževanje učiteljev, pouk tujega jezika, načrtovanje pouka, teorija kaosa, education, teacher training, foreign language learning, lesson planning, chaos theory Published: 10.07.2015; Views: 1717; Downloads: 112 Link to full text 
7. Evolution under alliancespecific cyclical invasion ratesMatjaž Perc, 2007, unpublished conference contribution Keywords: hrup, intenziteta hrupa, dilema zapornika, kaos, nelinearni dinamični sistemi, noise, spatiotemporal noise, intensity, prisoner's dilemma, chaos, nonlinear dynamic systems Published: 10.07.2015; Views: 903; Downloads: 21 Link to full text 
8. Cooperation out of noiseMatjaž Perc, 2007, unpublished conference contribution Keywords: hrup, intenziteta hrupa, dilema zapornika, kaos, nelinearni dinamični sistemi, noise, spatiotemporal noise, intensity, prisoner's dilemma, chaos, nonlinear dynamic systems Published: 10.07.2015; Views: 870; Downloads: 19 Link to full text 
9. Statistical Properties of Timedependent SystemsDiego Fregolente Mendes De Oliveira, 2012, doctoral dissertation Abstract: In the dissertation I have dealt with timedependent (nonautonomous) systems,
the conservative (Hamiltonian) as well as dissipative, and investigated their dynamical
and statistical properties. In conservative (Hamiltonian) timedependent systems the
energy is not conserved, whilst the Liouville theorem about the conservation of the phase
space volume still applies. We are interested to know, whether the system can gain
energy, and whether this energy can grow unbounded, up to infinity, and we are
interested in the system's behaviour in the mean, as well as its statistical
properties. An example of such a system goes back to the 1940s, when Fermi proposed
the acceleration of cosmic rays (in the first place protons) upon the collisions
with moving magnetic domains in the interstellar medium of our Galaxy,
and in other galaxies. He then proposed a simple mechanical onedimensional model,
the socalled FermiUlam Model (FUM), where a point particle is moving between two
rigid walls, one being at rest and the other one oscillating. If the oscillation
is periodic and smooth, it turned out in a nontrivial way, which is, in the
modern era of understanding the chaotic dynamical systems, well understood,
namely that the unbounded increasing of the energy (the socalled Fermi
acceleration) is not possible, due to the barriers in form of invariant tori,
which partition the phase space into regions, between which the transitions are
not possible. The research has then been extended to other simple dyanamical
systems, which have complex dynamics. The first was socalled bouncer model,
in which a point particle bounces off the oscillating platform in a gravitational
field. In this simple system the Fermi acceleration is possible. Later
the research was directed towards twodimensional billiard systems. It turned
out that the Fermi acceleration is possible in all such systems, which are at least
partially chaotic (of the mixed type), or even in a system that is integrable
as static, namely in case of the elliptic billiard. (The circle billiard
is an exception, because it is always integrable, as the angular momentum
is conserved even in timedependent case.) The study of timedependent systems
has developed strongly worldwide around the 1990s, in particular in 2000s,
and became one of the central topics in nonlinear dynamics. It turned out,
quite generally, but formal and implicit, in the sense of mathematical
existence theorems, that in nonautonomous Hamilton systems the energy can
grow unbounded, meaning that the system ``pumps" the energy from the environment
with which it interacts. There are many open questions: how does the energy
increase with time, in particular in the mean of some representative ensemble
of initial conditions (typically the phase space of twodimensional timedependent
billiards is fourdimensional.) It turned out that almost everywhere the power laws
apply, empirically, based on the numerical calculations, but with various
acceleration exponents. If the Fermi acceleration is not posssible, like e.g.
in the FUM, due to the invariant tori, then after a certain time of acceleration
stage the crossover into the regime of saturation takes place, whose
characteristics also follow the power laws. One of the central themes in
the dissertation is the study of these power laws, their critical exponents,
analytical relationships among them, using the scaling analysis
(Leonel, McClintock and Silva, Phys. Rev. Lett. 2004). Furthermore, the central
theme is the question, what happens, if, in a nonautonomous Hamilton system
which exhibits Fermi acceleration, we introduce dissipation, either
at the collisions with the walls (collisional dissipation) or
during the free motion (inflight dissipation, due to the viscosity
of the fluid or the drag force etc.). Dissipation typically transforms
the periodic points into point attractors and chaotic components into
chaotic attractors. The Fermi acceleration is always suppressed.
We are interested in the phase portraits of Keywords: nonlinear dynamics, dynamical systems, conservative and dissipative
systems, timedependent systems, Fermi acceleration, billiards, kicked systems, chaos, chaotic and periodic attractors, bifurcations, boundary crisis Published: 19.09.2012; Views: 2390; Downloads: 102 Full text (16,09 MB) 
10. 