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Dissertations / Theses on the topic 'Delay differential equations (DDEs)'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

Gallage, Roshini Samanthi. "Approximation Of Continuously Distributed Delay Differential Equations." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/theses/2196.

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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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2

Taylor, S. Richard. "Probabilistic Properties of Delay Differential Equations." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1183.

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Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, <em>i. e. </em> in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the dynamics of ensembles (statistical mechanics) and systems with uncertainty in the initial conditions. It is also the basis of ergodic theory--the study of probabilistic invariants of dynamical systems--which provides one framework for understanding chaotic systems whose time evolutions are erratic and for practical purposes unpredictable.

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3

Berntson, B. K. "Integrable delay-differential equations." Thesis, University College London (University of London), 2017. http://discovery.ucl.ac.uk/1566618/.

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Delay-differential equations are differential-difference equations in which the derivatives and shifts are taken with respect to the same variable. This thesis is concerned with these equations from the perspective of the theory of integrable systems, and more specifically, Painlevé equations. Both the classical Painlevé equations and their discrete analogues can be obtained as deautonomizations of equations solved by two-parameter families of elliptic functions. In analogy with this paradigm, we consider autonomous delay-differential equations solved by elliptic functions, delay-differentia

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4

Allen, Brenda. "Non-smooth differential delay equations." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390472.

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5

Fontana, Gaia. "Traffic waves and delay differential equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21211/.

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Questo elaborato si pone l'obiettivo di studiare il problema del traffico, concentrandosi su un modello semplificato in cui i veicoli sono confinati su una circonferenza e la cui velocità è determinata dal modello optimal velocity. Il discorso si sviluppa su tre capitoli: nel primo viene presentato il modello optimal velocity per il flusso del traffico e si procede a uno studio della stabilità lineare attorno al punto di equilibrio stazionario. Nel secondo capitolo lo stesso modello viene studiato nel limite termodinamico per un numero infinito di veicoli. Si ricava una soluzione costituita

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6

Ron, Eyal [Verfasser]. "Hysteresis-Delay Differential Equations / Eyal Ron." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1121588026/34.

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7

Zhang, Wenkui. "Numerical analysis of delay differential and integro-differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0011/NQ42489.pdf.

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8

Hines, Gwendolen. "Dependence of the attractor on the delay for delay-differential equations." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/28954.

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9

Bahar, Arifah. "Applications of stochastic differential equations and stochastic delay differential equations in population dynamics." Thesis, University of Strathclyde, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415294.

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10

Reiss, Markus. "Nonparametric estimation for stochastic delay differential equations." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964782480.

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11

Ballinger, George Henri. "Qualitative theory of impulsive delay differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ51178.pdf.

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12

Wille, David Richard. "The numerical solution of delay-differential equations." Thesis, University of Manchester, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.291519.

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13

Lumb, Patricia M. "Delay differential equations : detection of small solutions." Thesis, University of Chester, 2004. http://hdl.handle.net/10034/68595.

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This thesis concerns the development of a method for the detection of small solutions to delay differential equations. The detection of small solutions is important because their presence has significant influence on the analytical prop¬erties of an equation. However, to date, analytical methods are of only limited practical use. Therefore this thesis focuses on the development of a reliable new method, based on finite order approximations of the underlying infinite dimen¬sional problem, which can detect small solutions. Decisions (concerning the existence, or otherwise, of small solutions) ba

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14

Ezeofor, Victory S. "Analysis of differential-delay equations for biology." Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/39940/.

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In this thesis, we investigate the role of time delay in several differential-delay equation focusing on the negative autogenous regulation. We study these models for little or no delay to when the model has a very large delay parameter. We start with the logistic differential-delay equation applying techniques that would be used in subsequent chapters for other models being studied. A key goal of this research is to identify where the structure of the system does change. First, we investigate these models for critical point and study their behaviour close to these points. Of keen interest is

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15

Reiß, Markus. "Nonparametric estimation for stochastic delay differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14741.

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Sei (X(t), t>= -r) ein stationärer stochastischer Prozess, der die affine stochastische Differentialgleichung mit Gedächtnis dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, löst, wobei sigma>0, (W(t), t>=0) eine Standard-Brownsche Bewegung und L ein stetiges lineares Funktional auf dem Raum der stetigen Funktionen auf [-r,0], dargestellt durch ein endliches signiertes Maß a, bezeichnet. Wir nehmen an, dass eine Trajektorie (X(t), -r 0, konvergiert. Diese Rate ist schlechter als in vielen klassischen Fällen. Wir beweisen jedoch eine untere Schranke, die zeigt, dass keine Schätzung eine bessere Rate im Mi

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16

Zhou, Ziqian. "Statistical inference of distributed delay differential equations." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2173.

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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

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17

Ogrowsky, Arne [Verfasser]. "Random Differential Equations with Random Delay / Arne Ogrowsky." München : Verlag Dr. Hut, 2011. http://d-nb.info/1017353352/34.

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18

Nishiguchi, Junya. "Retarded functional differential equations with general delay structure." 京都大学 (Kyoto University), 2017. http://hdl.handle.net/2433/225381.

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19

Karoui, Abderrazek. "On the numerical solution of delay differential equations." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/7673.

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A numerical method for the treatment of non-vanishing lag state dependent delay differential equations is developed in this work. This method is based on a (5,6) Runge-Kutta formula pair. The delayed term is approximated by a three-point Hermite polynomial. In order to obtain a highly accurate numerical scheme, special attention is given to the characterization and the localization of the derivative jump discontinuities of the solution. Some real-life problems are used to test the new method and compare it with existing ones.

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20

Guillouzic, Steve. "Fokker-Planck approach to stochastic delay differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58279.pdf.

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21

Losson, Jérôme. "Multistability and probabilistic properties of differential delay equations." Thesis, McGill University, 1991. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60514.

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The dynamics of a class of nonlinear delay differential equations (D.D.E's) is studied. We focus attention on D.D.E's with a discrete delay used as models for production/destruction processes. The design of an electronic analog computer simulating an integrable D.D.E is presented. This computer is used to illustrate the presence of bistable solutions in the system. The multistability is investigated numerically with an analytic integration algorithm. Higher order multistability is reported, and the structure of basin boundaries in the space of initial functions is investigated. Pathological de

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22

Tannerah, Lamees Hassan. "Modelling a dairy herd using delay differential equations." Thesis, University of Liverpool, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427024.

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23

Swain, Robin. "The Morris-Lecar equations with delay /." Internet access available to MUN users only, 2003. http://collections.mun.ca/u?/theses,162993.

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24

Zhang, Yandong Sinha S. C. "Some techniques in the control of dynamic systems with periodically varying coefficients." Auburn, Ala., 2007. http://hdl.handle.net/10415/1346.

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25

Gimeno, i. Alquézar Joan. "Effective methods for recurrence solutions in delay differential equations." Doctoral thesis, Universitat de Barcelona, 2020. http://hdl.handle.net/10803/668438.

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This thesis deals with the jet transport for numerical integrators and the effective invariant object computation of delay differential equations. Firstly we study how automatic differentiation (AD) affects when they are applied to numerical integrators of ordinary differential equations (ODEs). We prove that the use of AD is exactly the same as considering the initial ODE and add new equations to the calculation of the variational flow up to a certain order. With this result we propose to detail the effective computation when these equations are affected by a delay. In particular

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26

René, Alexandre. "Spectral Solution Method for Distributed Delay Stochastic Differential Equations." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34327.

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Stochastic delay differential equations naturally arise in models of complex natural phenomena, yet continue to resist efforts to find analytical solutions to them: general solutions are limited to linear systems with additive noise and a single delayed term. In this work we solve the case of distributed delays in linear systems with additive noise. Key to our solution is the development of a consistent interpretation for integrals over stochastic variables, obtained by means of a virtual discretization procedure. This procedure makes no assumption on the form of noise, and would likely be use

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27

Bennett, Deborah. "Applications of delay differential equations in physiology and epidemiology." Thesis, University of Surrey, 2005. http://epubs.surrey.ac.uk/842713/.

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The primary aim of this thesis has been to study examples of the application of delay differential equations to both physiology and epidemiology. As such, the thesis has two main strands. The physiological application is represented by mathematical models of the glucose-insulin interaction in humans. We provide a detailed introduction to recent and current literature associated with this area, together with an overview of the physiological processes involved. Two systems explicitly incorporating a discrete delay are proposed and positivity and boundedness of solutions to these models are estab

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28

Weedermann, Marion. "On perturbations of delay-differential equations with periodic orbits." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/27972.

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29

Caberlin, Martin D. "Stiff ordinary and delay differential equations in biological systems." Thesis, McGill University, 2002. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=29416.

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The Santillan-Mackey model of the tryptophan operon was developed to characterize the anthranilate synthase activity in cultures of Escherichia coli. Similarly, the GABA reaction scheme was formulated to characterize the response of the GABAA receptor at a synapse, and the Hodgkin-Huxley model was developed to characterize the action potential of a squid giant axon. While the Hodgkin-Huxley model has been studied in great detail from a mathematical vantage, much less is known about the preceding two models in this regard. This work examines the stiffness of all three models; a novel perspectiv

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30

Dražková, Jana. "Stability of Neutral Delay Differential Equations and Their Discretizations." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2014. http://www.nusl.cz/ntk/nusl-234204.

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Disertační práce se zabývá asymptotickou stabilitou zpožděných diferenciálních rovnic a jejich diskretizací. V práci jsou uvažovány lineární zpožděné diferenciální rovnice s~konstantním i neohraničeným zpožděním. Jsou odvozeny nutné a postačující podmínky popisující oblast asymptotické stability jak pro exaktní, tak i diskretizovanou lineární neutrální diferenciální rovnici s konstantním zpožděním. Pomocí těchto podmínek jsou porovnány oblasti asymptotické stability odpovídajících exaktních a diskretizovaných rovnic a vyvozeny některé vlastnosti diskrétních oblastí stability vzhledem k měnícím

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31

Zhuang, Dawei. "Stability analysis of stochastic differential delay equations with jumps." Thesis, Swansea University, 2011. https://cronfa.swan.ac.uk/Record/cronfa42955.

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32

Kyrychko, Yuliya. "Qualitative analysis of solutions of some partial differential equations and equations with delay." Thesis, University of Surrey, 2004. http://epubs.surrey.ac.uk/844561/.

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This thesis is devoted to the qualitative analysis of solutions of partial differential N equations and delay partial differential equations with applications to population biology. The first part deals with the problem of finding the length scales for the Navier-Stokes system on a rotating sphere and for a class of generalized reaction-diffusion system on a planar domain. Since the reaction-diffusion system under investigation has many biological and physical applications, it is crucial to be able to prove a positivity preserving property for solutions of this system. Motivated by its applica

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33

McDaniel, Austin James. "The Effects of Time Delay on Noisy Systems." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/556867.

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We consider a general stochastic differential delay equation (SDDE) with multiplicative colored noise. We study the limit as the time delays and the correlation times of the noises go to zero at the same rate. First, we derive the limiting equation for the equation obtained by Taylor expanding the SDDE to first order in the time delays. The limiting equation contains a noise-induced drift term that depends on the ratios of the time delays to the correlation times of the noises. We prove that, under appropriate assumptions, the solution of the equation obtained by the Taylor expansion converges

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34

Alzabut, Jehad. "Periodic Solutions And Stability Of Linear Impulsive Delay Differential Equations." Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/2/12604901/index.pdf.

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In this thesis, we investigate impulsive differential systems with delays of the form And more generally of the form The dissertation consists of five chapters. The first chapter serves as introduction, contains preliminary considerations and assertions that will be encountered in the sequel. In chapter 2, we construct the adjoint systems and obtain the variation of parameters formulas of the solutions in terms of fundamental matrices. The asymptotic behavior of solutions of systems satisfying the Perron co

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35

Wulf, Volker. "Numerical analysis of delay differential equations undergoing a Hopf bifurcation." Thesis, University of Liverpool, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367052.

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36

Dvořáková, Stanislava. "The Qualitative and Numerical Analysis of Nonlinear Delay Differential Equations." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2011. http://www.nusl.cz/ntk/nusl-233952.

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Disertační práce formuluje asymptotické odhady řešení tzv. sublineárních a superlineárních diferenciálních rovnic se zpožděním. V těchto odhadech vystupuje řešení pomocných funkcionálních rovnic a nerovností. Dále práce pojednává o kvalitativních vlastnostech diferenčních rovnic se zpožděním, které vznikly diskretizací studovaných diferenciálních rovnic. Pozornost je věnována souvislostem asympotického chování řešení rovnic ve spojitém a diskrétním tvaru, a to v obecném i v konkrétních případech. Studována je rovněž stabilita numerické diskretizace vycházející z $\theta$-metody. Práce obsahuje

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37

Villegas, Caballero Manuel [Verfasser]. "Random Delay Differential Equations: Application to Biofilm Modeling / Manuel Villegas Caballero." München : Verlag Dr. Hut, 2012. http://d-nb.info/1020299525/34.

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38

Giordano, Gael. "Realization of Critical Eigenvalues for Systems of Linear Delay Differential Equations." Thesis, University of Ottawa (Canada), 2011. http://hdl.handle.net/10393/28893.

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This thesis is a step forward in the generalization of the Realization Theorem in the paper [15] by Buono and LeBlanc. In that theorem, the two authors study the link between the number of critical eigenvalues and the number of delays in a scalar delay differential equation of the form: y&d2;t =j=1lajy t-tj,a j∈R. In this thesis, we shall consider a system of p ( p ∈ N ) scalar delay-differential equations. That system can be written as: y&d2;t =j=1lMjy t-tj,M j∈Mp R. The goal is therefore to study the links between the number of critical eigenvalues, the number of delays

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39

Norton, Stewart J. "Noise induced changes to dynamic behaviour of stochastic delay differential equations." Thesis, University of Chester, 2008. http://hdl.handle.net/10034/72780.

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40

Khavanin, Mohammad. "The Method of Mixed Monotony and First Order Delay Differential Equations." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96643.

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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.<br>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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41

Kinnally, Michael Sean. "Stationary distributions for stochastic delay differential equations with non-negativity constraints." Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3355747.

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Thesis (Ph. D.)--University of California, San Diego, 2009.<br>Title from first page of PDF file (viewed June 23, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 114-116).

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42

Ospanov, Asset. "DELAY DIFFERENTIAL EQUATIONS AND THEIR APPLICATION TO MICRO ELECTRO MECHANICAL SYSTEMS." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5674.

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Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic s

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43

Malique, Md Abdul. "Numerical treatment of oscillatory delay and mixed functional differential equations arising in modelling." Thesis, University of Chester, 2012. http://hdl.handle.net/10034/311000.

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The pervading theme of this thesis is the development of insights that contribute to the understanding of whether certain classes of functional differential equation have solutions that are all oscillatory. The starting point for the work is the analysis of simple (linear autonomous) ordinary differential equations where existing results allow a full explanation of the phenomena. The Laplace transform features as a key tool in developing a theoretical background. The thesis goes on to explore the corresponding theory for delay equations, advanced equations and functional di erential equations

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44

Jánský, Jiří. "Delay Difference Equations and Their Applications." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-233892.

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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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45

Mensour, Boualem. "Dynamical invariants, multistability, controllability and synchronization in delay-differential and difference equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ28360.pdf.

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46

Paruchuri, Sai Tej. "Output Regulation of Systems Governed by Delay Differential Equations: Approximations and Robustness." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/98409.

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This thesis considers the problem of robust geometric regulation for tracking and disturbance rejection of systems governed by delay differential equations. It is well known that geometric regulation can be highly sensitive to system parameters and hence such designs are not always robust. In particular, when employing numerical approximations to delay systems, the resulting finite dimensional models inherit natural approximation errors that can impact robustness. This demonstrates this lack of robustness and then addresses robustness by employing versions of robust regulation that have been d

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47

O'Farrell, Hayley. "Temporal modelling of disease outbreaks using state space and delay differential equations." Thesis, University of Surrey, 2016. http://epubs.surrey.ac.uk/809649/.

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The two processes of outbreak identification and disease modelling are fundamental in the study of disease outbreaks affecting livestock and wildlife. Rapid detection and the implementation of appropriate preventative or control measures from an understanding of the mechanisms of disease spread may limit the impact of an outbreak. The performance of several on-line warning algorithms in their ability to detect outbreaks in both real-life and simulated data is investigated. A version of Farrington's well established outbreak detection algorithm, referred to as the EDS scheme is compared to appr

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48

McWilliams, Nairn Anthony. "Option pricing techniques under stochastic delay models." Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/5754.

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The Black-Scholes model and corresponding option pricing formula has led to a wide and extensive industry, used by financial institutions and investors to speculate on market trends or to control their level of risk from other investments. From the formation of the Chicago Board Options Exchange in 1973, the nature of options contracts available today has grown dramatically from the single-date contracts considered by Black and Scholes (1973) to a wider and more exotic range of derivatives. These include American options, which can be exercised at any time up to maturity, as well as options ba

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49

Norton, Trevor Michael. "Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays." Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/83825.

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Delay differential equations (DDEs) are often used to model systems with time-delayed effects, and they have found applications in fields such as climate dynamics, biosciences, engineering, and control theory. In contrast to ordinary differential equations (ODEs), the phase space associated even with a scalar DDE is infinite-dimensional. Oftentimes, it is desirable to have low-dimensional ODE systems that capture qualitative features as well as approximate certain quantitative aspects of the DDE dynamics. In this thesis, we present a Galerkin scheme for a broad class of DDEs and derive conver

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50

Ignatenko, Vera [Verfasser]. "Homoclinic and stable periodic solutions for differential delay equations from physiology / Vera Ignatenko." Gießen : Universitätsbibliothek, 2017. http://d-nb.info/113997727X/34.

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