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Search results for: chaotic dynamics
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Chaotic Dynamics and Bifurcations in Impact Systems
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REGULAR & CHAOTIC DYNAMICS
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Periodic and chaotic dynamics in a map‐based neuron model
PublicationMap-based neuron models are an important tool in modeling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on continuous or hybrid dynamical systems. However, due to their discrete nature, rigorous mathematical analysis might be challenging. We study a discrete model of neuronal dynamics introduced by Chialvo in 1995. In particular, we show that its reduced one-dimensional...
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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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Stochastic intervals for the family of quadratic maps
Open Research DataNumerical analysis of chaotic dynamics is a challenging task. The one-parameter families of logistic maps and closely related quadratic maps f_a(x)=a-x^2 are well-known examples of such dynamical systems. Determining parameter values that yield stochastic-like dynamics is especially difficult, because although this set has positive Lebesgue measure,...
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Nilpotent singularities and chaos: Tritrophic food chains
PublicationLocal bifurcation theory is used to prove the existence of chaotic dynamics in two well-known models of tritrophic food chains. To the best of our knowledge, the simplest technique to guarantee the emergence of strange attractors in a given family of vector fields consists of finding a 3-dimensional nilpotent singularity of codimension 3 and verifying some generic algebraic conditions. We provide the essential background regarding...
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One-dimensional chaos in a system with dry friction: analytical approach
PublicationWe introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of...
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Topological-numerical analysis of a two-dimensional discrete neuron model
PublicationWe conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times...
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Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System
PublicationIn this paper, we study a classical two-predators-one-prey model. The classical model described by a system of three ordinary differential equations can be reduced to a one-dimensional bimodalmap. We prove that this map has at most two stable periodic orbits. Besides, we describe the bifurcation structure of the map. Finally, we describe a mechanism that leads to bistable regimes. Taking this mechanism into account, one can easily...
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Long-range, water-mediated interaction between a moderately active antifreeze protein molecule and the surface of ice
PublicationUsing molecular dynamics simulations, we show that a molecule of moderately active antifreeze protein (type III AFP, QAE HPLC-12 isoform) is able to interact with ice in an indirect manner. This interaction occurs between the ice binding site (IBS) of the AFP III molecule and the surface of ice, and it is mediated by liquid water which separates these surfaces. As a result, the AFP III molecule positions itself at a specific orientation...
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The outdoor market places in the public spaces of a modern city = Miejsca handlu targowego w przestrzeni publicznej współczesnego miasta (vol.1)
PublicationNowadays the market in the public space has different meanings. One of the point of view concentrate on the market as a low attraction of the city, which make it more chaotic. Although there exist contrary point of view – to apply the outdoor markets and the fairs in the public space as a one of the main attraction dedicated for toursits and local people.
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Public spaces connecting cities. Green and Blue Infrastructures potential.
PublicationA city fragmentation causes a lot of negative effects in urban environment such as: disconnecting the environmental, functional and compositional relations, a loss of urban compactness, chaotic development, visual chaos, a domination of technical landscape, reduction of security. This is why one of main challenges for urban planners is to connect the fragmented structures by creating friendly, attractive and safe public space....
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Implementation of high-precision computation capabilities into the open-source dynamic simulation framework YADE
PublicationThis paper deals with the implementation of arbitrary precision calculations into the open-source discrete element framework YADE published under the GPL-2+ free software license. This new capability paves the way for the simulation framework to be used in many new fields such as quantum mechanics. The implementation details and associated gains in the accuracy of the results are discussed. Besides the "standard" double (64 bits)...
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„Space, architecture and infrastructure “in-between cities”.
PublicationThe article presents contemporary city problems, like division of the city, infrastructural barriers, empty spaces, chaotic development, cuting-off areas, threatening the city image and functioning. These problems can be best observed in the areas in-between cities. One of the main questions for urban planners and architects seems thus to be: how to connect the city spaces instead of creating the barriers, how to create the areas...
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A cryptic ribosome binding site, false signals in reporter systems and avoidance of protein translation chaos
PublicationThe expression of reporter gene may be induced by activation of cryptic signalling sequences, as we found while constructing the mutS-lacZ fusion gene. We cloned the Escherichia coli lacZ gene encoding beta-galactosidase into a plasmid vector carrying the Thermus thermophilus mutS gene. The clones expected to produce beta-galactosidase as the C-terminal fusion were selected for the complementation of beta-galactosidase activity...
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URBANIZATION OF METROPOLITAN AREAS – THE IMPORTANCE OF NEW SPATIAL DATA ANALYSIS TOOLS
PublicationNowadays, a rapid development of metropolises is connected with the pressure on urbanizing, which leads to a sharp increase in developed areas as well as urbanized areas. As this trend becomes more dynamic, cities sprawl beyond their administrative boundaries, causing spatial disintegration and hindering sustainable development of a given area. Increased dispersion of residential area results in extensive and chaotic spatial development,...
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Sustainable polymers targeted at the surgical and otolaryngological applications: Circularity and future
PublicationThe ongoing climate changes, high air and noise pollution have significant impact on humans’ health. This influence is especially visible in otolaryngology, which focuses on respiratory and hearing systems disfunctions. However, even though surgeries are done in response to diseases related to climate changes, they also have a negative impact on the environment, mostly connected with the inherence of single-use fossil fuel derived...
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Optimized Deep Learning Model for Flood Detection Using Satellite Images
PublicationThe increasing amount of rain produces a number of issues in Kerala, particularly in urban regions where the drainage system is frequently unable to handle a significant amount of water in such a short duration. Meanwhile, standard flood detection results are inaccurate for complex phenomena and cannot handle enormous quantities of data. In order to overcome those drawbacks and enhance the outcomes of conventional flood detection...
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Dzielnica Reprezentacyjna Gdyni i jej powojenne oraz współczesne interpretacje
PublicationThe concept of the Premiere District in Gdynia was first conceived in the 1920s and from that time on it constantly accompanied the history of the city. It derivated from the idea of creating a symbol of Poland's regaining independence after the first World War and the successful creation of the new port and city on the Baltic coast. As the result of that development, Gdynia was named the maritime capital of Poland and was treated...
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Parameter values for topological chaos in the reduced Chialvo model
Open Research DataThe following dataset is connected with a map-based neuron model introduced by D. Chialvo (Chaos, Solitons & Fractals, 5 (3-4) 1995). The reduced version of this model is a one dimensional discrete system which describes the evolution of the membrane voltage when the value of the second variable, the recovery variable, is fixed. We have recently...