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Search results for: FIRING MAP
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Firing map of an almost periodic input function
PublicationIn mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...
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Analysis of dynamics of a map-based neuron model via Lorenz maps
PublicationModeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large...
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Firing map for periodically and almost-periodically driven integrate-and-fire models: a dynamical systems approach
PublicationWe consider the Leaky Integrate-and-Fire and Perfect Integrator models of neuron’s dynamics with the input function being periodic and almost-periodic (in the sense of Stepanov). In particular we analyze properties and dynamics of the so-called firing map, which iterations give timings of consecutive spikes of a neuron. In case of a periodic input function we provide a detailed description of the sequence of interspike-intervals,...
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Connection of microcosm with macrocosm in Max Scheler's philosophy: man, logos and ethos
PublicationW eseju pokazałem znaczenie mikrokosmicznego wymiaru w ludzkim personalnym życiu. To jest w świecie Zachodu kompleksowa próba, aby uchwycić związek "mikrokosmosu" z "makrokosmosem w filozoficznym dziele Maxa Schelera. Następnie uwypukliłem, że z racji jego powiązania jako pojęcia "mikrokosmosu" z kwestią kształcenia, wtedy w indywidualnej ludzkiej osobie pojęcie to osiąga "prawo obywatelstwa" w Schelerowskiej...
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The Optimal Spindle Speed Map for Reduction of Chatter Vibration During Milling of Bow Thruster Blade
PublicationW artykule przedstwiono przykład wykorzystania procedury tworzenia mapy optymalnych prędkosci obrotowych w celu ograniczenia drgań samowzbudnych podczas frezowania płata śruby okrętowego steru strumieniowego.
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An absorbing set for the Chialvo map
PublicationThe classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...
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A Mechatronic System for Building the Map of Optimal Spindle Speeds During High Speed Milling of Flexible Details
PublicationW pracy przedstawiono mechatroniczny system tworzenia mapy optymalnych prędkości obrotowych wrzeciona w celu nadzorowania drgań typu chatter podczas frezowania szybkościowego przedmiotów podatnych. System ten składa się z części pomiarowej oraz części obliczeniowej, w której wykorzystuje się oprogramowanie autorskie i komercyjne. Na bazie uogólnionego warunku Liao-Younga utworzono mapy optymalnych prędkości obrotowych wrzeciona,...
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Inducing a map on homology from a correspondence
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Shadowing is generic---a continuous map case
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E-learning in tourism and hospitality: A map
PublicationThe impact of information and communication technologies (ICT) on tourism and hospitality industries has been widely recognized and investigated as a one of the major changes within the domains in the last decade: new ways of communicating with prospective tourists and new ways of purchasing products arisen are now part of the industries’ everyday life. Poor attention has been paid so far to the role played by new media in education...