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: 1177; Prenosov: 22 Povezava na celotno besedilo 
2. Effects of smallworld connectivity on noiseinduced temporal and spatial order in neural mediaMatjaž Perc, 2006, izvirni znanstveni članek Opis: We present an overview of possible effects of smallworld connectivity on noiseinduced temporal and spatial order in a twodimensional network of excitable neural media with FitzHughNagumo local dynamics. Smallworld networks are characterized by a given fraction of socalled longrange couplings or shortcut links that connect distant units of the system, while all other units are coupled in a diffusivelike manner. Interestingly, already a small fraction of these longrange couplings can have wideranging effects on the temporal as well as spatial noiseinduced dynamics of the system. Here we present two main effects. First, we show that the temporal order, characterized by the autocorrelation of a firingrate function, can be greatly enhanced by the introduction of smallworld connectivity, whereby the effect increases with the increasing fraction of introduced shortcut links. Second, we show that the introduction of longrange couplings induces disorderof otherwise ordered, spiralwavelike, noiseinduced patterns that can be observed by exclusive diffusive connectivity of spatial units. Thereby, already a small fraction of shortcut links is sufficient to destroy coherent pattern formation in the media. Although the two results seem contradictive, we provide an explanation considering the inherent scalefree nature of smallworld networks, which on one hand, facilitates signal transduction and thus temporal order in the system, whilst on the other hand, disrupts the internal spatial scale of the media thereby hindering the existence of coherent wavelike patterns. Additionally, the importance of spatially versus temporally ordered neural network functioning is discussed. Ključne besede: physics, complex systems, dynamical systems, noise, chaos, chaotic systems, chaos control, resonance Objavljeno: 07.06.2012; Ogledov: 1154; Prenosov: 57 Povezava na celotno besedilo 
3. Spatial coherence resonance in neuronal media with discrete local dynamicsMatjaž Perc, 2006, izvirni znanstveni članek Opis: We study effects of spatiotemporal additive noise on the spatial dynamics of excitable neuronal media that is locally modelled by a twodimensional map. We focus on the ability of noise to enhance a particular spatial frequency of the media in a resonant manner. We show that there exists an optimal noise intensity for which the inherent spatial periodicity of the media is resonantly pronounced, thus marking the existence of spatial coherence resonance in the studied system. Additionally, results are discussed in view of their possible biological importance. Ključne besede: physics, complex systems, dynamical systems, noise, spatial dynamics, chaos, chaotic systems, chaos control, resonance Objavljeno: 07.06.2012; Ogledov: 1397; Prenosov: 78 Povezava na celotno besedilo 
4. Fluctuating excitability : a mechanism for selfsustained information flow in excitable arraysMatjaž Perc, 2007, izvirni znanstveni članek Opis: We show that the fluctuating excitability of FitzHughNagumo neurons, constituting a diffusively coupled excitable array, can induce phase slips that lead to a symmetry break yielding a preferred spreading direction of excitatory events, thus enabling persistent selfsustained and selforganized information flow in a periodic array long after a localized stimulus perturbation has sized. Possible oscillation frequencies of the informationcarrying signal are expressed analytically, and necessary conditions for the phenomenon are derived. Our results suggest that cellular diversity in neural tissue is crucial for maintaining selfsustained and organized activity in the brain even in the absence of immediate stimuli, thus facilitating continuous evolution of its mechanisms for information retrieval and storage. Ključne besede: physics, complex systems, dynamical systems, flexibility, chaos, chaotic systems, oscillations, perturbation Objavljeno: 07.06.2012; Ogledov: 1201; Prenosov: 60 Povezava na celotno besedilo 
5. 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: 1421; Prenosov: 65 Povezava na celotno besedilo 
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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: 1120; Prenosov: 244 Celotno besedilo (1,05 MB) Gradivo ima več datotek! Več...

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9. 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: 888; Prenosov: 20 Povezava na celotno besedilo 
10. 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: 972; Prenosov: 43 Povezava na celotno besedilo 