1. The dynamics of human gaitMatjaž Perc, 2005, izvirni znanstveni članek Opis: We analyse the dynamics of human gait with simple nonlinear time series analysis methods that are appropriate for undergraduate courses. We show that short continuous recordings of the human locomotory apparatus possess properties typical of deterministic chaotic systems. To facilitate interest and enable the reproduction of presented results, as well as to promote applications of nonlinear time series analysis to other experimental systems, we provide userfriendly programs for each implemented method. Thus, we provide new insights into the dynamics of human locomotion, and make an effort to ease the inclusion of nonlinear time series analysis methods into the curriculum at an early stage of the educational process. Ključne besede: dynamic systems, chaotic systems, nonlinear dynamics, human gait, human locomotion Objavljeno: 01.06.2012; Ogledov: 1050; Prenosov: 21 Povezava na celotno besedilo 
2. Encyclopedia of complexity and systems scienceslovar, enciklopedija, leksikon, priročnik, atlas, zemljevid Opis: Encyclopedia of Complexity and Systems Science provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all fields of science and engineering. The science and tools of complexity and systems science include theories of selforganization, complex systems, synergetics, dynamical systems, turbulence, catastrophes, instabilities, nonlinearity, stochastic processes, chaos, neural networks, cellular automata, adaptive systems, and genetic algorithms. Examples of nearterm problems and major unknowns that can be approached through complexity and systems science include: The structure, history and future of the universe; the biological basis of consciousness; the integration of genomics, proteomics and bioinformatics as systems biology; human longevity limits; the limits of computing; sustainability of life on earth; predictability, dynamics and extent of earthquakes, hurricanes, tsunamis, and other natural disasters; the dynamics of turbulent flows; lasers or fluids in physics, microprocessor design; macromolecular assembly in chemistry and biophysics; brain functions in cognitive neuroscience; climate change; ecosystem management; traffic management; and business cycles. All these seemingly quite different kinds of structure formation have a number of important features and underlying structures in common. These deep structural similarities can be exploited to transfer analytical methods and understanding from one field to another. This unique work will extend the influence of complexity and system science to a much wider audience than has been possible to date. Ključne besede: cellular automata, complex networks, computational nanoscience, ecological complexity, ergodic theory, fractals, game theory, granular computing, graph theory, intelligent systems, perturbation theory, quantum information science, system dynamics, traffic management, chaos, climate modelling, complex systems, dynamical sistems, fuzzy theory systems, nonlinear systems, soft computing, stochastic processes, synergetics, selforganization, systems biology, systems science Objavljeno: 01.06.2012; Ogledov: 1464; Prenosov: 61 Povezava na celotno besedilo 
3. Transition from Gaussian to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma gameMatjaž Perc, 2007, izvirni znanstveni članek Opis: We study the impact of stochastic payoff variations with different distributions on the evolution of cooperation in the spatial prisoner's dilemma game. We find that Gaussiandistributed payoff variations are most successful in promoting cooperation irrespective of the temptation to defect. In particular, the facilitative effect of noise on the evolution of cooperation decreases steadily as the frequency of rare events increases. Findings are explained via an analysis of local payoff ranking violations. The relevance of results for economics and sociology is discussed. Ključne besede: stochastic systems, spatial resonance, stochastic payoff variations, nonlinear systems, noise, spatial dynamics, mathematical models, prisoner's dilemma Objavljeno: 07.06.2012; Ogledov: 1088; Prenosov: 50 Povezava na celotno besedilo 
4. Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systemsMarko Gosak, Matjaž Perc, 2007, izvirni znanstveni članek Opis: We show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance. In particular, additive Gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner. Results obtained for the logistic map and the Lorenz equations suggest that the presented mechanism of coherence resonance is valid beyond particularities of individual systems. We attribute the findings to the increasing attraction of imminent periodic orbits and the ability of noise to anticipate their existence and use a modified wavelet analysis to support our arguments. Ključne besede: chaotic systems, spatial resonance, coherence resonance, nonlinear systems, noise, spatial dynamics, mathematical models, bifurcation diagrame Objavljeno: 07.06.2012; Ogledov: 1273; Prenosov: 38 Povezava na celotno besedilo 
5. Thoughts out of noiseMatjaž Perc, 2006, izvirni znanstveni članek Opis: We study the effects of additive Gaussian noise on the behaviour of a simple spatially extended system, which is locally modelled by a nonlinear twodimensional iterated map describing neuronal dynamics. In particular, we focus on the ability of noise to induce spatially ordered patterns, i. e. the socalled noiseinduced pattern formation. For intermediate noise intensities, the spatially extended system exhibits ordered circular waves, thereby clearly manifesting the constructive role of random perturbations. The emergence of observed noiseinduced patterns is explained with simple arguments that are obtained by analysing the typical spatial scale of patterns evoked by various diffusion coefficients. Since discretetime systems are straightforward to implement and require modest computational capabilities, the present study describes one of the most fascinating and visually compelling examples of noiseinduced selforganization in nonlinear systems in an accessible way for graduate or even advanced undergraduate students attending a nonlinear dynamics course. Ključne besede: dynamic systems, chaotic systems, nonlinear dynamics, nonlinear systems, noise, nonlinear analyses Objavljeno: 07.06.2012; Ogledov: 786; Prenosov: 18 Povezava na celotno besedilo 
6. Visualizing the attraction of strange attractorsMatjaž Perc, 2005, strokovni članek Opis: We describe a simple new method that provides instructive insights into the dynamics of chaotic timecontinuous systems that yield strange attractors as solutions in the phase space. In particular, we show that the norm of the vector field component that is orthogonal to the trajectory is an excellent quantity for visualizing the attraction of strange attractors, thus promoting the understanding of their formation and overall structure. Furthermore, based on the existence of zero orthogonal field strengths in planes that form lowdimensional strange attractors, we also provide an innovative explanation for the origin of chaotic behaviour. For instructive purposes, we first apply the method to a simple limit cycle attractor, and then analyse two paradigmatic mathematical models for classical timecontinuous chaos. To facilitate the use of our method in graduate as well as undergraduate courses, we also provide userfriendly programs in which the presented theory is implemented. Ključne besede: dynamic systems, chaotic systems, nonlinear dynamics, attractors, strange attractors Objavljeno: 07.06.2012; Ogledov: 833; Prenosov: 31 Povezava na celotno besedilo 
7. Nonlinear time series analysis of the human electrocardiogramMatjaž Perc, 2005, strokovni članek Opis: We analyse the human electrocardiogram with simple nonlinear time series analysis methods that are appropriate for graduate as well as undergraduate courses. In particular, attention is devoted to the notions of determinism and stationarity in physiological data. We emphasize that methods of nonlinear time series analysis can be successfully applied only if the studied data set originates from a deterministic stationary system. After positively establishing the presence of determinism and stationarity in the studied electrocardiogram, we calculate the maximal Lyapunov exponent, thus providing interesting insights into the dynamics of the human heart. Moreover, to facilitate interest and enable the integration of nonlinear time series analysis methods into the curriculum at an early stage of the educational process, we also provide userfriendly programs for each implemented method. Ključne besede: dynamic systems, chaotic systems, nonlinear dynamics, electrocardiogram, human electrocardiogram, nonlinear analyses Objavljeno: 07.06.2012; Ogledov: 1016; Prenosov: 40 Povezava na celotno besedilo 
8. Statistical Properties of Timedependent SystemsDiego Fregolente Mendes De Oliveira, 2012, doktorska disertacija Opis: 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 Ključne besede: nonlinear dynamics, dynamical systems, conservative and dissipative
systems, timedependent systems, Fermi acceleration, billiards, kicked systems, chaos, chaotic and periodic attractors, bifurcations, boundary crisis Objavljeno: 19.09.2012; Ogledov: 1898; Prenosov: 72 Celotno besedilo (16,09 MB) 
9. The periodicity of the anticipative discrete demandsupply modelAndrej Škraba, Davorin Kofjač, Črtomir Rozman, 2006, izvirni znanstveni članek Ključne besede: cobweb, hiperincursivity, system dynamics, anticipative system, nonlinear system, Farey tree, chaos Objavljeno: 10.07.2015; Ogledov: 406; Prenosov: 14 Povezava na celotno besedilo 
10. Gap junctions and epileptic seizures  two sides of the same coin?Vladislav Volman, Matjaž Perc, Maxim Bazhenov, 2011, izvirni znanstveni članek Opis: Electrical synapses (gap junctions) play a pivotal role in the synchronization of neuronal ensembles which also makes them likely agonists of pathological brain activity. Although large body of experimental data and theoretical considerations indicate that coupling neurons by electrical synapses promotes synchronous activity (and thus is potentially epileptogenic), some recent evidence questions the hypothesis of gap junctions being among purely epileptogenic factors. In particular, an expression of interneuronal gap junctions is often found to be higher after the experimentally induced seizures than before. Here we used a computational modeling approach to address the role of neuronal gap junctions in shaping the stability of a network to perturbations that are often associated with the onset of epileptic seizures. We show that under some circumstances, the addition of gap junctions can increase the dynamical stability of a network and thus suppress the collective electrical activity associated with seizures. This implies that the experimentally observed postseizure additions of gap junctions could serve to prevent further escalations, suggesting furthermore that they are a consequence of an adaptive response of the neuronal network to the pathological activity. However, if the seizures are strong and persistent, our model predicts the existence of a critical tipping point after which additional gap junctions no longer suppress but strongly facilitate the escalation of epileptic seizures. Our results thus reveal a complex role of electrical coupling in relation to epileptiform events. Which dynamic scenario (seizure suppression or seizure escalation) is ultimately adopted by the network depends critically on the strength and duration of seizures, in turn emphasizing the importance of temporal and causal aspects when linking gap junctions with epilepsy. Ključne besede: epilepsy, nonlinear dynamics, electrical synapses, coupling, synchronization Objavljeno: 19.06.2017; Ogledov: 236; Prenosov: 169 Celotno besedilo (858,25 KB) Gradivo ima več datotek! Več...
