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Center Manifold Analysis of Delayed Lienard Equation and Its ApplicationsZhao, Siming 14 January 2010 (has links)
Lienard Equations serve as the elegant models for oscillating circuits. Motivated
by this fact, this thesis addresses the stability property of a class of delayed Lienard
equations. It shows the existence of the Hopf bifurcation around the steady state.
It has both practical and theoretical importance in determining the criticality of the
Hopf bifurcation. For such purpose, center manifold analysis on the bifurcation line
is required. This thesis uses operator differential equation formulation to reduce the
infinite dimensional delayed Lienard equation onto a two-dimensional manifold on
the critical bifurcation line. Based on the reduced two-dimensional system, the so
called Poincare-Lyapunov constant is analytically determined, which determines the
criticality of the Hopf bifurcation. Numerics based on a Matlab bifurcation toolbox
(DDE-Biftool) and Matlab solver (DDE-23) are given to compare with the theoretical
calculation. Two examples are given to illustrate the method.
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Statistical inference of distributed delay differential equationsZhou, Ziqian 01 August 2016 (has links)
In this study, we aim to develop new likelihood based method for estimating parameters of ordinary differential equations (ODEs) / delay differential equations (DDEs) models. Those models are important for modeling dynamical processes that are described in terms of their derivatives and are widely used in many fields of modern science, such as physics, chemistry, biology and social sciences. We use our new approach to study a distributed delay differential equation model, the statistical inference of which has been unexplored, to our knowledge. Estimating a distributed DDE model or ODE model with time varying coefficients results in a large number of parameters. We also apply regularization for efficient estimation of such models. We assess the performance of our new approaches using simulation and applied them to analyzing data from epidemiology and ecology.
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Approximation Of Continuously Distributed Delay Differential EquationsGallage, Roshini Samanthi 01 August 2017 (has links)
We establish a theorem on the approximation of the solutions of delay differential equations with continuously distributed delay with solutions of delay differential equations with discrete delays. We present numerical simulations of the trajectories of discrete delay differential equations and the dependence of their behavior for various delay amounts. We further simulate continuously distributed delays by considering discrete approximation of the continuous distribution.
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The Method of Mixed Monotony and First Order Delay Differential Equations / The Method of Mixed Monotony and First Order Delay Differential EquationsKhavanin, Mohammad 25 September 2017 (has links)
In this paper I extend the method of mixed monotony, to construct monotone sequences that converge to the unique solution of an initial value delay differential equation. / En este artículo se prueba una generalización del método de monotonía mixta, para construir sucesiones monótonas que convergen a la solución única de una ecuación diferencial de retraso con valor inicial.
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Modelo matemático da resposta imune à infecção pelo vírus HIV-1. / Immune response mathematical model to HIV virus infection.Rossi, Marcelo 02 April 2008 (has links)
Avanços recentes nos conhecimentos sobre a infecção viral e AIDS tem levado pacientes soropositivos a uma melhor qualidade de vida. A determinação de quais populações celulares ou qual mecanismo imunológico seja mais relevante para instalação da epidemia conduz a novos patamares de possibilidades de novas drogas antiretrovirais e tratamento mais eficientes. O uso de modelagem matemática, para a epidemiologia, correlaciona indivíduos (neste caso células) e doença (o vírus) através de equações diferenciais, onde se quer observar as condições necessárias para a instalação ou não da doença. Neste trabalho, observou-se através das simulações, que o componente mais importante, depois do linfócito TCD4+, é a célula macrófago (por ser um reservatório de proliferação viral), que a infecção ocorre várias vezes ao longo do tempo (devido o processo de apresentação de antígenos) e que os linfócitos CTL são ineficientes em erradicar a infecção pelo vírus HIV-1, que pode ser um simples fenômeno de co-adaptação. / Recent advances in knowledge about the viral infection and AIDS seropositive patients has led to a better life quality. The determination of what people or cellular immune mechanism which is more relevant for the epidemic installation leads to new levels of possibilities to new antiretroviral drugs discovers and more efficient treatment. Mathematical modeling use on epidemiology, correlates individuals (this case cells) and illness (the virus) through differential equations, where want to observe the conditions necessary to the installation or not the disease. In this study, it was observed through simulations, that the most important component, after lymphocyte CD4 T cells, macrophages is the cell (as a reservoir of viral proliferation) that the infection occurs repeatedly over time (because of the antigen presenting process) and CTL lymphocytes are inefficient in eradicating the infection by HIV-1, which may be a simple phenomenon of co-adaptation.
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Oscillatory Dynamics of the Actin CytoskeletonWestendorf, Christian 28 November 2012 (has links)
No description available.
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Modelo matemático da resposta imune à infecção pelo vírus HIV-1. / Immune response mathematical model to HIV virus infection.Marcelo Rossi 02 April 2008 (has links)
Avanços recentes nos conhecimentos sobre a infecção viral e AIDS tem levado pacientes soropositivos a uma melhor qualidade de vida. A determinação de quais populações celulares ou qual mecanismo imunológico seja mais relevante para instalação da epidemia conduz a novos patamares de possibilidades de novas drogas antiretrovirais e tratamento mais eficientes. O uso de modelagem matemática, para a epidemiologia, correlaciona indivíduos (neste caso células) e doença (o vírus) através de equações diferenciais, onde se quer observar as condições necessárias para a instalação ou não da doença. Neste trabalho, observou-se através das simulações, que o componente mais importante, depois do linfócito TCD4+, é a célula macrófago (por ser um reservatório de proliferação viral), que a infecção ocorre várias vezes ao longo do tempo (devido o processo de apresentação de antígenos) e que os linfócitos CTL são ineficientes em erradicar a infecção pelo vírus HIV-1, que pode ser um simples fenômeno de co-adaptação. / Recent advances in knowledge about the viral infection and AIDS seropositive patients has led to a better life quality. The determination of what people or cellular immune mechanism which is more relevant for the epidemic installation leads to new levels of possibilities to new antiretroviral drugs discovers and more efficient treatment. Mathematical modeling use on epidemiology, correlates individuals (this case cells) and illness (the virus) through differential equations, where want to observe the conditions necessary to the installation or not the disease. In this study, it was observed through simulations, that the most important component, after lymphocyte CD4 T cells, macrophages is the cell (as a reservoir of viral proliferation) that the infection occurs repeatedly over time (because of the antigen presenting process) and CTL lymphocytes are inefficient in eradicating the infection by HIV-1, which may be a simple phenomenon of co-adaptation.
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Diferenciální rovnice se zpožděním v dynamických systémech / Delay Differential Equations in Dynamic SystemsDokyi, Martha January 2021 (has links)
Tato práce je přehledem zpožděných diferenciálních rovnic v dynamických systémech. Počínaje obecným přehledem zpožděných diferenciálních rovnic představujeme koncept zpožděných diferenciálů a použití jeho modelů, od biologie a populační dynamiky po fyziku a inženýrství. Poskytneme také přehled Dynamické systémy a diferenciální rovnice zpoždění v dynamických systémech. Oblastí pro modelování s rovnicemi zpožďovacích diferenciálů je Epidemiologie. Důraz je kladen na vývoj epidemiologického modelu Susceptible-Infected-Removed (SIR) bez časového zpoždění. Analyzujeme naše dva modely v rovnováze a lokální stabilitě pomocí předpokládaných dat COVID -19. Výsledky by byly porovnány mezi modelem bez zpoždění a modelem se zpožděním.
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Regularization by White Noise for Stochastic Functional Differential EquationsBachmann, Stefan 13 December 2019 (has links)
No description available.
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Delay Difference Equations and Their Applications / Delay Difference Equations and Their ApplicationsJánský, Jiří January 2010 (has links)
Disertační práce se zabývá vyšetřováním kvalitativních vlastností diferenčních rovnic se zpožděním, které vznikly diskretizací příslušných diferenciálních rovnic se zpožděním pomocí tzv. $\Theta$-metody. Cílem je analyzovat asymptotické vlastnosti numerického řešení těchto rovnic a formulovat jeho horní odhady. Studována je rovněž stabilita vybraných numerických diskretizací. Práce obsahuje také srovnání s dosud známými výsledky a několik příkladů ilustrujících hlavní dosažené výsledky.
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