Wyszukiwarka
Wyniki wyszukiwania dla: chaos
-
CHAOS
Czasopisma -
CHAOS
Czasopisma -
CHAOS SOLITONS & FRACTALS
Czasopisma -
Nilpotent singularities and chaos: Tritrophic food chains
PublikacjaLocal 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...
-
Polynomial Chaos Expansion in Bio- and Structural Mechanics
PublikacjaThis thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the repair...
-
Polynomial Chaos Expansion in Bio-and Structural Mechanics
PublikacjaThis monograph presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the...
-
Spike patterns and chaos in a map-based neuron model
PublikacjaThe work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour....
-
Chaos Theory and Applications
Czasopisma -
One-dimensional chaos in a system with dry friction: analytical approach
PublikacjaWe 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...
-
Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: II
Publikacja -
Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: I
Publikacja -
Chaos, Solitons and Fractals: X
Czasopisma -
Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublikacjaIn a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...
-
Rapid Multi-band Patch Antenna Yield Estimation Using Polynomial Chaos-Kriging
PublikacjaYield estimation of antenna systems is important to check their robustness with respect to the uncertain sources. Since the Monte Carlo sampling-based real physics simulation model evaluations are computationally intensive, this work proposes the polynomial chaos-Kriging (PC-Kriging) metamodeling technique for fast yield estimation. PC-Kriging integrates the polynomial chaos expansion (PCE) as the trend function of Kriging metamodel...
-
Regression points in non-intrusive polynomial chaos expansion method and D-optimal design
PublikacjaThe paper addresses selected issues of uncertainty quantification in the modelling of a system containing surgical mesh used in ventral hernia repair. Uncertainties in the models occur e.g. due to variability of abdominal wall properties among others. In order to include them, a non-intrusive regression-based polynomial chaos expansion method is employed. Its accuracy depends on the choice of regression points. In the study a relation...
-
In search of excellence in organizational strategy formation in the context of deterministic chaos: the case of Grupa Azoty
Publikacja -
Airfoil Design Under Uncertainty Using Non-Intrusive Polynomial Chaos Theory and Utility Functions
PublikacjaFast and accurate airfoil design under uncertainty using non-intrusive polynomial chaos (NIPC) expansions and utility functions is proposed. The NIPC expansions provide a means to efficiently and accurately compute statistical information for a given set of input variables with associated probability distribution. Utility functions provide a way to rigorously formulate the design problem. In this work, these two methods are integrated...
-
A cryptic ribosome binding site, false signals in reporter systems and avoidance of protein translation chaos
PublikacjaThe 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...
-
Sensitivity analysis based on non-intrusive regression-based polynomial chaos expansion for surgical mesh modelling
PublikacjaThe modelling of a system containing implants used in ventral hernia repair and human tissue suffers from many uncertainties. Thus, a probabilistic approach is needed. The goal of this study is to define an efficient numerical method to solve non-linear biomechanical models supporting the surgeon in decisions about ventral hernia repair. The model parameters are subject to substantial variability owing to, e.g., abdominal wall...
-
Parameter values for topological chaos in the reduced Chialvo model
Dane BadawczeThe 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...
-
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Czasopisma -
Analysis of dynamics of a map-based neuron model via Lorenz maps
PublikacjaModeling 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...
-
Topological-numerical analysis of a two-dimensional discrete neuron model
PublikacjaWe 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...
-
Combinatorial-topological framework for the analysis of global dynamics
Publikacja -
Computing algebraic transfer entropy and coupling directions via transcripts
PublikacjaMost random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer...
-
Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate-blood pressure coupling quantified by entropy-based indices
PublikacjaWe introduce an entropy-based classification method for pairs of sequences (ECPS) for quantifying mutual dependencies in heart rate and beat-to-beat blood pressure recordings. The purpose of the method is to build a classifier for data in which each item consists of two intertwined data series taken for each subject. The method is based on ordinal patterns and uses entropy-like indices. Machine learning is used to select a subset...
-
Rigorous numerics for critical orbits in the quadratic family
PublikacjaWe develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of one-dimensional maps fa(x)=a−x2. We illustrate the effectiveness of our approach by constructing a dynamically defined partition P of the parameter interval Ω=[1.4,2] into almost 4 million subintervals, for each of which we compute to high precision the...
-
Chaosu się uczmy
Publikacja -
Teoria chaosu, MAT2017
Kursy OnlineTeoria chaosu, MAT2017, kierunek matematyka, studia II stopnia, semestr III
-
Teoria chaosu 2023/2024
Kursy Online -
Theoretical and computational analysis of nonlinear fractional integro-differential equations via collocation method
Publikacja -
Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
PublikacjaFractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
-
Crystallization of space: Space-time fractals from fractal arithmetic
PublikacjaFractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated...
-
Analytical and numerical solution of a coupled KdV - MKdV system.
PublikacjaTransformację Darboux zastosowano do całkowania układów równań KdV - MKdV.Reprezentacja Laxa używa 2x2 macierzowe zagadnienie spektralne drugiego rzędu. Numeryczną metodę wprowadzono razem z dowodem zbieżności.
-
Układy dynamiczne i teoria chaosu
Kursy Online -
Układy dynamiczne i wstęp do chaosu
Kursy Online -
Układy dynamiczne i teoria chaosu (wykład)
Kursy Online -
APPLICATION OF COHEN'S CLASS TIME-FREQUENCY DISTRIBUTIONS IN THE BELOUSOV–ZHABOTINSKY REACTION ANALYSIS
Publikacja -
Kwadratura koła czyli o próbach poszukiwania odniesień ładu do chaosu, czy też chaosu do ładu w przebiegu rozwoju myśli architektonicznej.
PublikacjaStwierdzić należy ze smutkiem że architektura jest ingerencją w naturę z natury rzeczy! Na ile da się zapanować nad nieładem w urządzaniu świata w przyszłości.
-
Teoria chaosu wykład i seminarium 2022/2023
Kursy OnlineTeoria chaosu (MAT2017) Specjalność: Analityk danych (WFTiMS), II stopnia, stacjonarne, 2021/2022 - zimowy (sem. 3)
-
Wpływ teorii chaosu na niektóre tradycyjne stanowiska ontologiczne oraz na spór o redukcjonizm
PublikacjaTeoria chaosu stanowi nie tylko nowy paradygmat w nauce, ale także inspirację do badań filozoficznych nad rzeczywistością. W artykule podjęto próbę zarysowania głównych założeń teorii chaosu oraz określenia jej wpływu na niektóre tradycyjne stanowiska ontologiczne oraz spór o redukcjonizm. Z punktu widzenia ontologii, w dynamice nieliniowej szczególnie interesujący jest powrót do ciągłościowego monoizmu w opozycji do atomizmu....
-
Barbara Wikieł dr
Osoby -
Justyna Signerska-Rynkowska dr inż.
OsobySince 2021 visiting assistant professor in Dioscuri Centre in Topological Data Analysis (Institute of Mathematics of the Polish Academy of Sciences, IMPAN) Since 2016 assistant professor at Gdańsk University of Technology, Faculty of Applied Physics and Mathematics, Department of Differential Equations and Mathematics Applications 2020 - 2023 Principal Investigator in "SONATA" grant “Challenges of low-dimensional...
-
Landscape protection - the challenge for sustainable planning
PublikacjaGrowing spatial chaos reminds us of the need for systematic, complex approaches related to environmental and landscape issues within different planning, organizational, operational, legal and political activities. It has been proved, that LVIA within EIA plays an important role in the enhancement of the spatial planning system, and that there is a need to use the potential of EIA/LVIA in spatial development and management. But...
-
Periodic and chaotic dynamics in a map‐based neuron model
PublikacjaMap-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...
-
Residue-Pole Methods for Variability Analysis of S-parameters of Microwave Devices with 3D FEM and Mesh Deformation
PublikacjaThis paper presents a new approach for variability analysis of microwave devices with a high dimension of uncertain parameters. The proposed technique is based on modeling an approximation of system by its poles and residues using several modeling methods, including ordinary kriging, Adaptive Polynomial Chaos (APCE), and Support Vector Machine Regression (SVM). The computational cost is compared with the traditional Monte-Carlo...
-
Analysis of spontaneous electrochemical oscillations by the wavelet transformation method.
PublikacjaW pracy została przedstawiona nowa metoda analizy oscylacji prądu, które związane są z anodowym roztwarzaniem metali. Transformacja falkowa jest używana do rozdzielenia i analizy spektralnej pojedynczych przebiegów elementarnych komponentów oscylacji elektronicznych. Zastosowana została metoda rozkładu energii oscylacji analogiczna do funkcji spektralnej gęstości mocy.Wykazano, że chaotyczne składniki (chaos Shilnikova)...
-
A comprehensive approach to double inverted pendulum modelling
PublikacjaThe problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used....
-
Public spaces connecting cities. Green and Blue Infrastructures potential.
PublikacjaA 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....
-
Methodological challenges in social entrepreneurship – on the nexus of economics and management area
PublikacjaIn this paper we make an attempt distinguishing challenges in SE research agenda in Polish and beyond. We identify what can impede the development of this area in Polish discourse These challenges vary in scope. They involve the dilemma between either economics or management as disciplinary settings. Also the understanding of social economy as such determines the chaos. Additionally, divergences in paradigms where researchers situate...