Wyniki wyszukiwania dla: CHAOS
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CHAOS
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CHAOS
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CHAOS SOLITONS & FRACTALS
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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...
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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...
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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...
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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....
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Chaos Theory and Applications
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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...
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Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: II
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Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: I
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Chaos, Solitons and Fractals: X
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
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