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2. Qualitative Studies of Some Polynomial Systems of Ordinary Differential EquationsMaša Dukarić, 2016, doktorska disertacija Opis: This doctoral dissertation is devoted to the studies of some qualitative properties of certain polynomial systems of ordinary differential equations. The main problems that are considered in this thesis are the problems of integrability and cyclicity. Some results on the classification of the global phase portraits of a family of cubic systems are presented as well. In the first chapter basic notions and results of the qualitative theory of systems of ODE's are introduced. Since one of important tools for our study of these problems is the commutative computational algebra, some main notions and properties of polynomial ideals and their varieties, including various algorithms related to them, are also presented in the introduction. In the second chapter methods for investigation of trajectories near degenerated singularities are presented. They are further used for the classification of global phase portraits of a family of cubic systems with the nilpotent center at the origin. In the third chapter the main problem of these thesis is studied, the problem of integrability. The problem of integrability which is connected to the problem of distinguishing between a center and a focus is studied for two different families of cubic polynomial systems of ODE's. With the computational algebra approach the necessary conditions for the existence of the first integral of these systems were obtained. For all but one condition was proven, using various approaches, the existence of the first integrals. The center problem for the real systems can be generalized to the complex systems. The origin of the system obtained after the complexification of the real system is the socalled 1:1 resonant singular point, from which one additional generalization follows. This is the generalization to the p:q resonant center. In the third chapter the :3 resonant singular point of a quadratic family of complex systems is studied. The fourth chapter is devoted to the study of the problem of integrability of a three dimensional polynomial system with quadratic nonlinearities. The problem of existence of two independent first integrals and the existence of one first integral in the system was investigated. In the last chapter local bifurcations of limit cycles of a family of cubic systems are studied. Estimations for the number of limit cycles bifurcated from each components of the center variety are obtained. Ključne besede: planar systems of ODE's, higher dimensional systems of ODE's, phase portrait, nilpotent center, limit cylces, Poincaré compactification, center problem, Bautin ideal, focus quantities, timereversibility, integrability problem, Darboux method, linearizability, limit cycle, cyclicity Objavljeno: 19.07.2016; Ogledov: 1160; Prenosov: 129 Celotno besedilo (12,26 MB) 
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4. Implementation of hard realtime embedded control systemsMatjaž Colnarič, Domen Verber, Roman Gumzej, Wolfgang A. Halang, 1998, samostojni znanstveni sestavek ali poglavje v monografski publikaciji Opis: Although the domain of hard realtime systems has been thoroughly elaborated in the academic sphere, embedded computer control systems  being an important in mechatronic design  are seldom dealt with consistemntly. Often, offtheshelf computer systems are used, with no guarantee that they will be able to meet the requirements specified. In this paper, a design for embedded control systems is presented. particulary, the paper deals with the hardware architecture and design details, the operating sustem, and the highlevel realtime language support. It is shown how estimates of process runtimes necessary for schedulability analysis can be acquired on the basis of deterministic behavior of the hardware platform. Ključne besede: kontrolni sistemi, realni čas, mikrokontrolerji, programski jeziki, embedded compuer control systems, hard realtime systems, microcontrollers, transputers, earliestdeadlinefirst scheduling, realtime programming languages Objavljeno: 10.07.2015; Ogledov: 662; Prenosov: 82 Povezava na celotno besedilo 
5. 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: 2302; Prenosov: 100 Celotno besedilo (16,09 MB) 
6. Introducing nonlinear time series analysis in undergraduate coursesMatjaž Perc, 2006, strokovni članek Opis: This article is written for undergraduate students and teachers who would like to get familiar with basic nonlinear time series analysis methods. We present a stepbystep study of a simple example and provide userfriendly programs that allow an easy reproduction of presented results. In particular, we study an artificial time series generated by the Lorenz system. The mutual information and false nearest neighbour method are explained in detail, and used to obtain the best possible attractor reconstruction. Subsequently, the times series is tested for stationarity and determinism, which are both important properties that assure correct interpretation of invariant quantities that can be extracted from the data set. Finally, as the most prominent invariant quantity that allows distinguishing between regular and chaotic behaviour, we calculate the maximal Lyapunov exponent. By following the above steps, we are able to convincingly determine that the Lorenz system is chaotic directly from the generated time series, without the need to use the differential equations. Throughout the paper, emphasis on clearcut guidance and a handson approach is given in order to make the reproduction of presented results possible also for undergraduates, and thus encourage them to get familiar with the presented theory. Ključne besede: nonlinear systems, nonlinear time series analyses, physics education Objavljeno: 07.06.2012; Ogledov: 983; Prenosov: 23 Povezava na celotno besedilo 
7. Singing of Neoconocephalus robustus as an example of deterministic chaos in insectsTina P. Benko, Matjaž Perc, 2007, izvirni znanstveni članek Opis: We use nonlinear time series analysis methods to analyse the dynamics of the soundproducing apparatus of the katydid Neoconocephalus robustus. We capture the dynamics by analysing a recording of the singing activity. First, we reconstruct the phase space from the sound recording and test it against determinism and stationarity. After confirming determinism and stationarity, we show that the maximal Lyapunov exponent of the series is positive, which is a strong indicator for the chaotic behaviour of the system. We discuss that methods of nonlinear time series analysis can yield instructive insights and foster the understanding of acoustic communication among insects. Ključne besede: chaotic systems, chaos, time series, time series analyses, insect sounds, katydid Objavljeno: 07.06.2012; Ogledov: 1291; Prenosov: 314 Celotno besedilo (1,05 MB) Gradivo ima več datotek! Več...

8. Establishing the stochastic nature of intracellular calcium oscillations from experimental dataMatjaž Perc, Anne K. Green, C. Jane Dixon, Marko Marhl, 2008, izvirni znanstveni članek Opis: Calcium has been established as a key messenger in both intra and intercellular signaling. Experimentally observed intracellular calcium responses to different agonists show a variety of behaviors from simple spiking to complex oscillatory regimes. Here we study typical experimental traces of calcium oscillations in hepatocytes obtained in response to phenylephrine and ATP. The traces were analyzed with methods of nonlinear time series analysis in order to determine the stochastic/deterministic nature of the intracellular calcium oscillations. Despite the fact that the oscillations appear, visually, to be deterministic yet perturbed by noise, our analyses provide strong evidence that the measured calcium traces in hepatocytes are prevalently of stochastic nature. In particular, bursting calcium oscillations are temporally correlated Gaussian series distorted by a monotonic, instantaneous, timeindependent function, whilst the spiking behavior appears to have a dynamical nonlinear component whereby the overall determinism level is still low. The biological importance of this finding is discussed in relation to the mechanisms incorporated in mathematical models as well as the role of stochasticity and determinism at cellular and tissue levels which resemble typical statistical and thermodynamic effects in physics. Ključne besede: dynamic systems, stochastic processes, cellular signaling, calcium oscillations, time series analyses, noise, temporal correlation Objavljeno: 07.06.2012; Ogledov: 1252; Prenosov: 103 Povezava na celotno besedilo 
9. Marketing across culturesJeanClaude Usunier, 2000, učbenik za višje in visoke šole Ključne besede: marketing, convergence, international marketing, globalization, market, integration, consumption, local communities, regional economics, consumer, culture, dynamic systems, time, space, interactions, behavior, intercultural communication, decision, product policy, managing, relativism, variables, business environment, distribution, sales promotion, personal selling, business communication, international exchange, relationship marketing, market research, public relations, bargaining, textbooks, case study Objavljeno: 01.06.2012; Ogledov: 2287; Prenosov: 107 Povezava na celotno besedilo 
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