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1.
The dynamics of human gait
Matjaž Perc, 2005, original scientific article

Abstract: 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 user-friendly 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.
Keywords: dynamic systems, chaotic systems, nonlinear dynamics, human gait, human locomotion
Published: 01.06.2012; Views: 1050; Downloads: 21
URL Link to full text

2.
Effects of small-world connectivity on noise-induced temporal and spatial order in neural media
Matjaž Perc, 2006, original scientific article

Abstract: We present an overview of possible effects of small-world connectivity on noise-induced temporal and spatial order in a two-dimensional network of excitable neural media with FitzHugh-Nagumo local dynamics. Small-world networks are characterized by a given fraction of so-called long-range couplings or shortcut links that connect distant units of the system, while all other units are coupled in a diffusive-like manner. Interestingly, already a small fraction of these long-range couplings can have wide-ranging effects on the temporal as well as spatial noise-induced dynamics of the system. Here we present two main effects. First, we show that the temporal order, characterized by the autocorrelation of a firing-rate function, can be greatly enhanced by the introduction of small-world connectivity, whereby the effect increases with the increasing fraction of introduced shortcut links. Second, we show that the introduction of long-range couplings induces disorderof otherwise ordered, spiral-wave-like, noise-induced 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 scale-free nature of small-world 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 wave-like patterns. Additionally, the importance of spatially versus temporally ordered neural network functioning is discussed.
Keywords: physics, complex systems, dynamical systems, noise, chaos, chaotic systems, chaos control, resonance
Published: 07.06.2012; Views: 1034; Downloads: 46
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3.
Spatial coherence resonance in neuronal media with discrete local dynamics
Matjaž Perc, 2006, original scientific article

Abstract: We study effects of spatiotemporal additive noise on the spatial dynamics of excitable neuronal media that is locally modelled by a two-dimensional 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.
Keywords: physics, complex systems, dynamical systems, noise, spatial dynamics, chaos, chaotic systems, chaos control, resonance
Published: 07.06.2012; Views: 1239; Downloads: 58
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4.
Fluctuating excitability : a mechanism for self-sustained information flow in excitable arrays
Matjaž Perc, 2007, original scientific article

Abstract: We show that the fluctuating excitability of FitzHugh-Nagumo 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 self-sustained and self-organized information flow in a periodic array long after a localized stimulus perturbation has sized. Possible oscillation frequencies of the information-carrying 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 self-sustained 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.
Keywords: physics, complex systems, dynamical systems, flexibility, chaos, chaotic systems, oscillations, perturbation
Published: 07.06.2012; Views: 1064; Downloads: 50
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5.
Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systems
Marko Gosak, Matjaž Perc, 2007, original scientific article

Abstract: 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.
Keywords: chaotic systems, spatial resonance, coherence resonance, nonlinear systems, noise, spatial dynamics, mathematical models, bifurcation diagrame
Published: 07.06.2012; Views: 1275; Downloads: 38
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6.
Flights towards defection in economic transactions
Matjaž Perc, 2007, original scientific article

Abstract: We show that Lévy distributed variations of payoffs in the prisoner's dilemma game impede cooperation as the frequency of rare events increases. Lévy flights thus facilitate defection, but also uphold the evolutionary process, arguably maintaining a healthy level of competitiveness amongst the agents.
Keywords: chaotic systems, game theory, Lévy process, cooperation, social welfare
Published: 07.06.2012; Views: 1002; Downloads: 45
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7.
Singing of Neoconocephalus robustus as an example of deterministic chaos in insects
Tina P. Benko, Matjaž Perc, 2007, original scientific article

Abstract: We use nonlinear time series analysis methods to analyse the dynamics of the sound-producing 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.
Keywords: chaotic systems, chaos, time series, time series analyses, insect sounds, katydid
Published: 07.06.2012; Views: 1028; Downloads: 187
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8.
Microeconomic uncertainties facilitate cooperative alliances and social welfare
Matjaž Perc, 2007, original scientific article

Abstract: We show that microeconomic chaotic variations of payoffs in the prisoner's dilemma game maintain cooperation over a broad range of defection temptation values where otherwise economic stalemate reigns. Thus, unpredictability at micro scales impedes mutual defection that inflicts social poverty.
Keywords: chaotic systems, game theory, microeconomic chaos, cooperation, social welfare
Published: 07.06.2012; Views: 1002; Downloads: 51
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9.
Thoughts out of noise
Matjaž Perc, 2006, original scientific article

Abstract: We study the effects of additive Gaussian noise on the behaviour of a simple spatially extended system, which is locally modelled by a nonlinear two-dimensional iterated map describing neuronal dynamics. In particular, we focus on the ability of noise to induce spatially ordered patterns, i. e. the so-called noise-induced 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 noise-induced patterns is explained with simple arguments that are obtained by analysing the typical spatial scale of patterns evoked by various diffusion coefficients. Since discrete-time systems are straightforward to implement and require modest computational capabilities, the present study describes one of the most fascinating and visually compelling examples of noise-induced self-organization in nonlinear systems in an accessible way for graduate or even advanced undergraduate students attending a nonlinear dynamics course.
Keywords: dynamic systems, chaotic systems, nonlinear dynamics, nonlinear systems, noise, nonlinear analyses
Published: 07.06.2012; Views: 787; Downloads: 18
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10.
Visualizing the attraction of strange attractors
Matjaž Perc, 2005, professional article

Abstract: We describe a simple new method that provides instructive insights into the dynamics of chaotic time-continuous 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 low-dimensional 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 time-continuous chaos. To facilitate the use of our method in graduate as well as undergraduate courses, we also provide user-friendly programs in which the presented theory is implemented.
Keywords: dynamic systems, chaotic systems, nonlinear dynamics, attractors, strange attractors
Published: 07.06.2012; Views: 836; Downloads: 32
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