Dissertations / Theses on the topic 'Differential system state equations'
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Foley, Dawn Christine. "Applications of State space realization of nonlinear input/output difference equations." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/16818.
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Li, Bo. "Steady State Solutions for a System of Partial Differential Equations Arising from Crime Modeling." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/hmc_theses/78.
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I consider a model for the control of criminality in cities. The model was developed during my REU at UCLA. The model is a system of partial differential equations that simulates the behavior of criminals and where they may accumulate, hot spots. I have proved a prior bounds for the partial differential equations in both one-dimensional and higher dimensional case, which proves the attractiveness and density of criminals in the given area will not be unlimitedly high. In addition, I have found some local bifurcation points in the model.
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Smario, David J. "Multicorrelation analysis and state space reconstruction /." Online version of thesis, 1994. http://hdl.handle.net/1850/11443.
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Ye, Jinglong. "Infinite semipositone systems." Diss., Mississippi State : Mississippi State University, 2009. http://library.msstate.edu/etd/show.asp?etd=etd-07072009-132254.
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Zhang, Zhengyang. "A class of state-dependent delay differential equations and applications to forest growth." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0062/document.
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Cette thèse est consacrée à l'étude d'une classe d'équations différentielles à retard dépendant de l'état -- ces équations provenant d'un modèle structuré en taille. La principale motivation de cette thèse provient de la volonté d'ajuster les paramètres du système d'équations étudiées vis-à-vis des données générées par un simulateur de forêts, appelé SORTIE. Deux types de forêts sont étudiés ici: d'une part une forêt ne comportant qu'une seule espèce d'arbre, et d'autre part une forêt comportant deux espèces d'arbres (au chapitre 2). Les simulations numériques du système d'équations correspondent relativement bien aux données générées par SORTIE, ce qui montre que le système considéré peut être utilisé afin d'écrire la dynamique de populations d'une forêt. De plus, un modèle plus étendu prenant en compte la position spatiale des arbres est proposé dans le chapitre 2, dans le cas de forêts possédant deux espèces d'arbres. Les simulations numériques de ce modèle permettent de visualiser la propagation spatiale des forêts. Les chapitres 3 et 4 se concentrent sur l'analyse mathématique des équations différentielles à retard considérées. Les propriétés du semi-flot associé au système sont étudiées au chapitre 3, où l'on démontre en particulier que ce semi-flot n'est pas continu en temps. Le caractère dissipatif et borné du semi-flot, pour des modèles de forêts comportant une ou deux espèces d'arbres, est étudié dans le chapitre 4. En outre, afin d'étudier la dynamique de population d'une forêt (d'une seule espèce d'arbre) après l'introduction d'un parasite, nous construisons dans le chapitre 5 un système proie-prédateur dont la proie (à savoir la forêt) est modélisée par le système d'équations différentielles à retard dépendant de l'état étudié auparavant, et dont le prédateur (à savoir le parasite) est modélisé par une équation différentielle ordinaire. De nombreuses simulations numériques associées à différents scénarios sont faites, afin d'explorer le comportement complexe des solutions du au couplage proie-prédateur et les équations à retard dépendant de l'étatThis thesis is devoted to the studies of a class of state-dependent delay differential equations. This class of equations is derived from a size-structured model.The motivation comes from the parameter fittings of this system to a forest simulator called SORTIE. Cases of both single species forest and two-species forest are considered in Chapter 2. The numerical simulations of the system correspond relatively very well to the forest data generated by SORTIE, which shows that this system is able to be used to describe the population dynamics of forests. Moreover, an extended model considering the spatial positions of trees is also proposed in Chapter 2 for the two-species forest case. From the numerical simulations of this spatial model one can see the diffusion of forests in space. Chapter 3 and 4 focus on the mathematical analysis of the state-dependent delay differential equations. The properties of semiflow generated by this system are studied in Chapter 3, where we find that this semiflow is not time-continuous. The boundedness and dissipativity of the semiflow for both single species model and multi-species model are studied in Chapter 4. Furthermore, in order to study the population dynamics after the introduction of parasites into a forest, a predator-prey system consisting of the above state-dependent delay differential equation (describing the forest) and an ordinary differential equation (describing the parasites) is constructed in Chapter 5 (only the single species forest is considered here). Numerical simulations in several scenarios and cases are operated to display the complex behaviours of solutions appearing in this system with the predator-prey relation and the state-dependent delay
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Ali, Jaffar. "Multiple positive solutions for classes of elliptic systems with combined nonlinear effects." Diss., Mississippi State : Mississippi State University, 2008. http://library.msstate.edu/etd/show.asp?etd=etd-07082008-153843.
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Bramburger, Jason. "Steady State/Hopf Interactions in the Van Der Pol Oscillator with Delayed Feedback." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24325.
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In this thesis we consider the traditional Van der Pol Oscillator with a forcing dependent on a delay in feedback. The delay is taken to be a nonlinear function of both position and velocity which gives rise to many different types of bifurcations. In particular, we study the Zero-Hopf bifurcation that takes place at certain parameter values using methods of centre manifold reduction of DDEs and normal form theory. We present numerical simulations that have been accurately predicted by the phase portraits in the Zero-Hopf bifurcation to confirm our numerical results and provide a physical understanding of the oscillator with the delay in feedback.
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Zeng, Honghai. "A web-based high performance simulation system for transport and retention of dissolved contaminants in soils." Diss., Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-10082002-144653.
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Nguyen, Hoan Kim Huynh. "Volterra Systems with Realizable Kernels." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11153.
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We compare an internal state method and a direct Runge-Kutta method for solving Volterra integro-differential equations and Volterra delay differential equations. The internal state method requires the kernel of the Volterra integral to be realizable as an impulse response function. We discover that when applicable, the internal state method is orders of magnitude more efficient than the direct numerical method. However, constructing state representation for realizable kernels can be challenging at times; therefore, we propose a rational approximation approach to avoid the problem. That is, we approximate the transfer function by a rational function, construct the corresponding linear system, and then approximate the Volterra integro-differential equation. We show that our method is convergent for the case where the kernel is nuclear. We focus our attention on time-invariant realizations but the case where the state representation of the kernel is a time-variant linear system is briefly discussed.Ph. D.
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Trimeloni, Thomas. "Accelerating Finite State Projection through General Purpose Graphics Processing." VCU Scholars Compass, 2011. http://scholarscompass.vcu.edu/etd/175.
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The finite state projection algorithm provides modelers a new way of directly solving the chemical master equation. The algorithm utilizes the matrix exponential function, and so the algorithm’s performance suffers when it is applied to large problems. Other work has been done to reduce the size of the exponentiation through mathematical simplifications, but efficiently exponentiating a large matrix has not been explored. This work explores implementing the finite state projection algorithm on several different high-performance computing platforms as a means of efficiently calculating the matrix exponential function for large systems. This work finds that general purpose graphics processing can accelerate the finite state projection algorithm by several orders of magnitude. Specific biological models and modeling techniques are discussed as a demonstration of the algorithm implemented on a general purpose graphics processor. The results of this work show that general purpose graphics processing will be a key factor in modeling more complex biological systems.
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Pittayakanchit, Weerapat. "The Global Stability of the Solution to the Morse Potential in a Catastrophic Regime." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/hmc_theses/72.
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Swarms of animals exhibit aggregations whose behavior is a challenge for mathematicians to understand. We analyze this behavior numerically and analytically by using the pairwise interaction model known as the Morse potential. Our goal is to prove the global stability of the candidate local minimizer in 1D found in A Primer of Swarm Equilibria. Using the calculus of variations and eigenvalues analysis, we conclude that the candidate local minimizer is a global minimum with respect to all solution smaller than its support. In addition, we manage to extend the global stability condition to any solutions whose support has a single component. We are still examining the local minimizers with multiple components to determine whether the candidate solution is the minimum-energy configuration.
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Swatzel, James Paul. "A partial differential equation to model the Tacoma Narrows Bridge failure." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2631.
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The purpose of this thesis was to examine a partial differential equation to model the Tacoma Narrows bridge failure. This thesis will examine the equation developed by Lazer and McKenna to model a suspension bridge in no wind.
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Tribastone, Mirco. "Scalable analysis of stochastic process algebra models." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4629.
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The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results.
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Correa, Diego Paolo Ferruzzo. "Symmetric bifurcation analysis of synchronous states of time-delay oscillators networks." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/3/3139/tde-29122014-180651/.
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In recent years, there has been increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry, patterns can emerge in these networks; as a consequence, a part of the system might repeat itself, and properties of this symmetric subsystem represent the whole dynamics. In this thesis, an analysis of a second order N-node time-delay fully connected network is made. This study is carried out using symmetry groups. The existence of multiple eigenvalues forced by symmetry is shown, as well as the possibility of uncoupling the linearization at equilibria, into irreducible representations due to the symmetry. The existence of steady-state and Hopf bifurcations in each irreducible representation is also proved. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. A finite set of frequencies ω is also determined, which might correspond to Hopf bifurcations in each case for critical values of the delay. Although we restrict our attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal.Nos últimos anos, tem havido um crescente interesse em estudar redes de osciladores acopladas com retardo de tempo uma vez que estes ocorrem em muitas aplicações da vida real. Em muitos casos, simetria e padrões podem surgir nessas redes; em consequência, uma parte do sistema pode repetir-se, e as propriedades deste subsistema simétrico representam a dinâmica da rede toda. Nesta tese é feita uma análise de uma rede de N nós de segunda ordem totalmente conectada com atraso de tempo. Este estudo é realizado utilizando grupos de simetria. É mostrada a existência de múltiplos valores próprios forçados por simetria, bem como a possibilidade de desacoplamento da linearização no equilíbrio, em representações irredutíveis. É também provada a existência de bifurcações de estado estacionário e Hopf em cada representação irredutível. São usados três modelos diferentes para analisar a dinâmica da rede: o modelo de fase completa, o modelo de fase, e o modelo de diferença de fase. É também determinado um conjunto finito de frequências ω, que pode corresponder a bifurcações de Hopf em cada caso, para valores críticos do atraso. Apesar de restringir a nossa atenção para nós de segunda ordem, os resultados podem ser estendido para redes de ordem superior, desde que o tempo de atraso nas conexões entre nós permanece igual.
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Nie, Tianyang. "Stochastic differential equations with constraints on the state : backward stochastic differential equations, variational inequalities and fractional viability." Thesis, Brest, 2012. http://www.theses.fr/2012BRES0047.
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Le travail de thèse est composé de trois thèmes principaux : le premier étudie l'existence et l'unicité pour des équations différentielles stochastiques (EDS) progressives-rétrogrades fortement couplées avec des opérateurs sous-différentiels dans les deux équations, dans l’équation progressive ainsi que l’équation rétrograde, et il discute également un nouveau type des inégalités variationnelles partielles paraboliques associées, avec deux opérateurs sous-différentiels, l’un agissant sur le domaine de l’état, l’autre sur le co-domaine. Le second thème est celui des EDS rétrogrades sans ainsi qu’avec opérateurs sous-différentiels, régies par un mouvement brownien fractionnaire avec paramètre de Hurst H> ½. Il étend de manière rigoureuse les résultats de Hu et Peng (SICON, 2009) aux inégalités variationnelles stochastiques rétrogrades. Enfin, le troisième thème met l’accent sur la caractérisation déterministe de la viabilité pour les EDS régies par un mouvement brownien fractionnaire. Ces trois thèmes de recherche mentionnés ci-dessus ont en commun d’étudier des EDS avec contraintes sur le processus d’état. Chacun des trois sujets est basé sur une publication et des manuscrits soumis pour publication, respectivementThis PhD thesis is composed of three main topics: The first one studies the existence and the uniqueness for fully coupled forward-backward stochastic differential equations (SDEs) with subdifferential operators in both the forward and the backward equations, and it discusses also a new type of associated parabolic partial variational inequalities with two subdifferential operators, one acting over the state domain and the other over the co-domain. The second topic concerns the investigation of backward SDEs without as well as with subdifferential operator, both driven by a fractional Brownian motion with Hurst parameter H> 1/2. It extends in a rigorous manner the results of Hu and Peng (SICON, 2009) to backward stochastic variational inequalities. Finally, the third topic focuses on a deterministic characterisation of the viability for SDEs driven by a fractional Brownian motion. The three research topics mentioned above have in common to study SDEs with state constraints. The discussion of each of the three topics is based on a publication and on submitted manuscripts, respectively
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Gauthier, Genevieve Carleton University Dissertation Mathematics and Statistics. "Multilevel bilinear system of stochastic differential equations." Ottawa, 1995.
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Müller, Thorsten G. "Modeling complex systems with differential equations." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10236319.
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Kadamani, Sami M. "USFKAD: An Expert System For Partial Differential Equations." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001144.
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Weickert, J. "Navier-Stokes equations as a differential-algebraic system." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800942.
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Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.
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Ntwoku, Stephane Ntuomou. "Dynamic transformer protection a novel approach using state estimation." Thesis, Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/45879.
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Transformers are very important parts of any electrical network, and their size increase so does their price. Protecting these important devices is a daunting task due to the wide variety of operating conditions. This thesis develops a new protection scheme based on state estimation.The foundation upon which our protection scheme is built is the modeling of the single phase transformer system of equations. The transformer equations are composed of polynomial and differential equations and this system of equations involving the transformer's electrical quantities are modeled into a system of equations such that highest degree of each of the system's equations is quadratic―in a process named Quadratization and then integrated using a technique called Quadratic integration to give a set of algebraic companion equations that can be solved numerically to determine the health of the transformer.
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Tidefelt, Henrik. "Differential-algebraic equations and matrix-valued singular perturbation." Doctoral thesis, Linköpings universitet, Reglerteknik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-51653.
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With the arrival of modern component-based modeling tools for dynamic systems, the differential-algebraic equation form is increasing in popularity as it is general enough to handle the resulting models. However, if uncertainty is allowed in the equations — no matter how small — this thesis stresses that such equations generally become ill-posed. Rather than deeming the general differential-algebraic structure useless up front due to this reason, the suggested approach to the problem is to ask what assumptions that can be made in order to obtain well-posedness. Here, “well-posedness” is used in the sense that the uncertainty in the solutions should tend to zero as the uncertainty in the equations tends to zero. The main theme of the thesis is to analyze how the uncertainty in the solution to a differential-algebraic equation depends on the uncertainty in the equation. In particular, uncertainty in the leading matrix of linear differential-algebraic equations leads to a new kind of singular perturbation, which is referred to as “matrix-valued singular perturbation”. Though a natural extension of existing types of singular perturbation problems, this topic has not been studied in the past. As it turns out that assumptions about the equations have to be made in order to obtain well-posedness, it is stressed that the assumptions should be selected carefully in order to be realistic to use in applications. Hence, it is suggested that any assumptions (not counting properties which can be checked by inspection of the uncertain equations) should be formulated in terms of coordinate-free system properties. In the thesis, the location of system poles has been the chosen target for assumptions. Three chapters are devoted to the study of uncertain differential-algebraic equations and the associated matrix-valued singular perturbation problems. Only linear equations without forcing function are considered. For both time-invariant and time-varying equations of nominal differentiation index 1, the solutions are shown to converge as the uncertainties tend to zero. For time-invariant equations of nominal index 2, convergence has not been shown to occur except for an academic example. However, the thesis contains other results for this type of equations, including the derivation of a canonical form for the uncertain equations. While uncertainty in differential-algebraic equations has been studied in-depth, two related topics have been studied more passingly. One chapter considers the development of point-mass filters for state estimation on manifolds. The highlight is a novel framework for general algorithm development with manifold-valued variables. The connection to differential-algebraic equations is that one of their characteristics is that they have an underlying manifold-structure imposed on the solution. One chapter presents a new index closely related to the strangeness index of a differential-algebraic equation. Basic properties of the strangeness index are shown to be valid also for the new index. The definition of the new index is conceptually simpler than that of the strangeness index, hence making it potentially better suited for both practical applications and theoretical developments.
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Chow, Tanya L. M., of Western Sydney Macarthur University, and Faculty of Business and Technology. "Systems of partial differential equations and group methods." THESIS_FBT_XXX_Chow_T.xml, 1996. http://handle.uws.edu.au:8081/1959.7/43.
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This thesis is concerned with the derivation of similarity solutions for one-dimensional coupled systems of reaction - diffusion equations, a semi-linear system and a one-dimensional tripled system. The first area of research in this thesis involves a coupled system of diffusion equations for the existence of two distinct families of diffusion paths. Constructing one-parameter transformation groups preserving the invariance of this system of equations enables similarity solutions for this coupled system to be derived via the classical and non-classical procedures. This system of equation is the uncoupled in the hope of recovering further similarity solutions for the system. Once again, one-parameter groups leaving the uncoupled system invariant are obtained, enabling similarity solutions for the system to be elicited. A one-dimensional pattern formation in a model of burning forms the next component of this thesis. The primary focus of this area is the determination of similarity solutions for this reaction - diffusion system by means of one-parameter transformation group methods. Consequently, similarity solutions which are a generalisation of the solutions of the one-dimensional steady equations derived by Forbes are deduced. Attention in this thesis is then directed toward a semi-linear coupled system representing a predator - prey relationship. Two approaches to solving this system are made using the classical procedure, leading to one-parameter transformation groups which are instrumental in elicting the general similarity solution for this system. A triple system of equations representing a one-dimensional case of diffusion in the presence of three diffusion paths constitutes the next theme of this thesis. In association with the classical and non-classical procedures, the derivation of one-parameter transformation groups leaving this system invariant enables similarity solutions for this system to be deduced. The final strand of this thesis involves a one- dimensional case of the general linear system of coupled diffusion equations with cross-effects for which one-parameter transformation group methods are once more employed. The one-parameter groups constructed for this system prove instrumental in enabling the attainment of similarity solutions for this system to be accomplishedFaculty of Business and Technology
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Yereniuk, Michael A. "Global Approximations of Agent-Based Model State Changes." Digital WPI, 2020. https://digitalcommons.wpi.edu/etd-dissertations/614.
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How can we model global phenomenon based on local interactions? Agent-Based (AB) models are local rule-based discrete method that can be used to simulate complex interactions of many agents. Unfortunately, the relative ease of implementing the computational model is often counter-balanced by the difficulty of performing rigorous analysis to determine emergent behaviors. Calculating existence of fixed points and their stability is not tractable from an analytical perspective and can become computationally expensive, involving potentially millions of simulations. To construct meaningful analysis, we need to create a framework to approximate the emergent, global behavior. Our research has been devoted to developing a framework for approximating AB models that move via random walks and undergo state transitions. First, we developed a general method to estimate the density of agents in each state for AB models whose state transitions are caused by neighborhood interactions between agents. Second, we extended previous random walk models of instantaneous state changes by adding a cumulative memory effect. In this way, our research seeks to answer how memory properties can also be incorporated into continuum models, especially when the memory properties effect state changes on the agents. The state transitions in this type of AB model is primarily from the agents’ interaction with their environment. These modeling frameworks will be generally applicable to many areas and can be easily extended.
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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 approaches based on the Kalman Filter, namely a Prediction Interval approach and three types of CUSUM scheme. All the schemes are able to successfully identify outbreaks and we find that no single approach appears to outperform the others in all the measures considered. However the EDS scheme is the most efficient in detecting outbreaks promptly and one of the CUSUM schemes is best at producing consistent warnings throughout the outbreak period. In addition we formulate deterministic models describing the transmission dynamics of the midge-borne disease bluetongue, with cattle and sheep as hosts. The models take the form of delay differential equations and incorporate the incubation time of bluetongue in cattle, sheep and midges, and also the larval developmental time of midges. An autonomous model assuming midges to be active year round and a periodic model allowing midge activity to vary with the seasons are analysed. The transmission of the disease via midge diffusion and migration is studied in detail and the effects of vaccination are also considered. Important findings include the need for prompt diagnosis of latent infection and appropriate action before the animal becomes infectious, and the need for measures that reduce insect bites. This reinforces the importance of timely identification of disease outbreaks in order for effective intervention to be possible.
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Smith, Eric Paul. "Analytical upstream collocation solution of a quadratic forced steady-state convection-diffusion equation." Boise, Idaho : Boise State University, 2009. http://scholarworks.boisestate.edu/td/29/.
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Lee, Hwasung. "Strominger's system on non-Kähler hermitian manifolds." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef.
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In this thesis, we investigate the Strominger system on non-Kähler manifolds. We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holomorphically trivial canonical bundles. We will then consider explicit examples when M can be realized as a principal torus fibration over a Kähler surface S. We will solve the Strominger system on such construction which also includes manifolds of topology (k−1)(S²×S⁴)#k(S³×S³). We will investigate the anomaly cancellation condition on the principal torus fibration M. The anomaly cancellation condition reduces to a complex Monge-Ampère-type PDE, and we will prove existence of solution following Yau’s proof of the Calabi-conjecture [Yau78], and Fu and Yau’s analysis [FY08]. Finally, we will discuss the physical aspects of our work. We will discuss the Strominger system using α'-expansion and present a solution up to (α')¹-order. In the α'-expansion approach on a principal torus fibration, we will show that solving the anomaly cancellation condition in topology is necessary and sufficient to solving it analytically. We will discuss the potential problems with α'-expansion approach and consider the full Strominger system with the Hull connection. We will show that the α'-expansion does not correctly capture the behaviour of the solution even up to (α')¹-order and should be used with caution.
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Baugh, James Emory. "Group analysis of a system of reaction-diffusion equations." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/28554.
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Hottovy, Scott. "The Smoluchowski-Kramers Approximation for Stochastic Differential Equations with Arbitrary State Dependent Friction." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293564.
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In this dissertation a class of stochastic differential equations is considered in the limit as mass tends to zero, called the Smoluchowski-Kramers limit. The Smoluchowski-Kramers approximation is useful in simplifying the dynamics of a system. For example, the problems of calculating of rates of chemical reactions, describing dynamics of complex systems with noise, and measuring ultra small forces, are simplified using the Smoluchowski-Kramers approximation. In this study, we prove strong convergence in the small mass limit for a multi-dimensional system with arbitrary state-dependent friction and noise coefficients. The main result is proved using a theory of convergence of stochastic integrals developed by Kurtz and Protter. The framework of the main theorem is sufficiently arbitrary to include systems of stochastic differential equations driven by both white and Ornstein-Uhlenbeck colored noises.
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Stanistreet, Timothy Francis. "Numerical methods for first order partial differential equations describing steady-state forming processes." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.398232.
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Yousept, Irwin. "Optimal control of partial differential equations involving pointwise state constraints: regularization and applications." Göttingen Cuvillier, 2008. http://d-nb.info/990426513/04.
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Dutra, Dimas Abreu. "Maximum a posteriori joint state path and parameter estimation in stochastic differential equations." Universidade Federal de Minas Gerais, 2014. http://hdl.handle.net/1843/BUOS-9S3H9D.
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A wide variety of phenomena of engineering and scientific interest are of a continuous-time nature and can be modeled by stochastic differential equations (SDEs), which represent the evolution of the uncertainty in the states of a system. For systems of this class, some parameters of the SDE might be unknown and the measured data often includes noise, so state and parameter estimators are needed to perform inference and further analysis using the system state path. One such application is the flight testing of aircraft, in which flight path reconstruction or some other data smoothing technique is used before proceeding to the aerodynamic analysis or system identification. The distributions of SDEs which are nonlinear or subject to non-Gaussian measurement noise do not admit tractable analytic expressions, so state and parameter estimators for these systems are often approximations based on heuristics, such as the extended and unscented Kalman smoothers, or the prediction error method using nonlinear Kalman filters. However, the Onsager Machlup functional can be used to obtain fictitious densities for the parameters and state-paths of SDEs with analytic expressions. In this thesis, we provide a unified theoretical framework for maximum a posteriori (MAP) estimation of general random variables, possibly infinitedimensional, and show how the OnsagerMachlup functional can be used to construct the joint MAP state-path and parameter estimator for SDEs. We also prove that the minimum energy estimator, which is often thought to be the MAP state-path estimator, actually gives the state paths associated to the MAP noise paths. Furthermore, we prove that the discretized MAP state-path and parameter estimators, which have emerged recently as powerful alternatives to nonlinear Kalman smoothers, converge hypographically as the discretization step vanishes. Their hypographical limit, however, is the MAP estimator for SDEs when the trapezoidal discretization is used and the minimum energy estimator when the Euler discretization is used, associating different interpretations to each discretized estimate. Example applications of the proposed estimators are also shown, with both simulated and experimental data. The MAP and minimum energy estimators are compared with each other and with other popular alternatives.Uma grande variedade de fenômenos de interesse para engenharia e ciência são a tempo contínuo por natureza e podem ser modelados por equações diferenciais estocásticas (EDEs), que representam a evolução da incerteza nos estados do sistema. Para sistemas dessa classe, alguns parâmetros da EDE podem ser desconhecidos e os dados coletados frequentemente incluem ruídos, de modo que estimatores de esstados e parâmetros são necessários para realizar inferência e análises adicionais usando a trajetória dos estados do sistema. Uma dessas aplicações é em ensaios em voo de aeronaves, para os quais reconstrução de trajetória de voo ou outras técnicas de suavização são utilizadas antes de se proceder para análise aerodinâmica ou identificação de sistemas. As distribuições de EDEs não lineares ou sujeitas a ruído de medição não Gaussiano não admitem expressões analíticas utilizáveis, o que leva a estimadores de estados e parâmetros para esses sistemas a basearem-se em heurísticas como os suavizadores de Kalman estendido e unscented, ou o método de predição de erro utilizando filtros de Kalman não lineares. No entanto, o funcional de OnsagerMachlup pode ser utilizado para obter densidades fictícias conjuntas para trajetórias de estado e parâmetros de EDEs com expressões analíticas. Nesta tese, um arcabouço teórico unificado é desenvolvido para estimação máxima a posteriori (MAP) de variáveis aleatórias genéricas, possivelmente infinito-dimensionais, e é mostrado como o funcional de OnsagerMachlup pode ser utilizado para a construção do estimador MAP conjunto de trajetórias de estado e parâmetros de EDEs. Também é provado que o estimador de mínima energia, comumente confundido com com o estimador de MAP, obtém as trajetórias de estado associadas às trajetórias de ruído MAP. Além disso, é provado que os estimadores conjuntos de trajetória de estados e parâmetros MAP discretizados, que emergiram recentemente como alternativas poderosas para os estimadores de Kalman não lineares, convergem hipograficamente à medida que o passo de discretização diminue. O seu limite hipográfico, no entanto, é o estimador MAP para EDEs quando a discretização trapezoidal é utilizada e o estimador de mínima energia quando a discretização de Euler é utilizada, associando interpretações diferentes a cada estimativa discretizada. Exemplos de aplicações dos estimadores propostos são apresentadas com dados simulados e experimentais, nas quais os estimadores MAP e de mínima energia são comparados entre si e com alternativas mais bem sedimentadas.
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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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Zakirova, Ksenia V. "Perturbation Dynamics on Moving Chains." Scholarship @ Claremont, 2015. http://scholarship.claremont.edu/hmc_theses/90.
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Chain dynamics have gained renewed interest recently, following the release of a viral YouTube video showcasing a phenomenon called the chain fountain. Recent work in the field shows that there exists unexplained behavior in newly proposed chain systems. We consider a general system of a chain traveling at constant velocity in an external force field and derive steady state solutions for the time invariant shape of the chain. Perturbing the solution introduces moving waves along the steady state shape with components that propagate along and against the direction of travel of the chain. Furthermore, we develop a numerical model using a discrete approximation of the chain in order to empirically test our results. The behavior of the chain fountain and related chain systems is discussed in the context of these findings.
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Huang, Weifeng. "INVESTIGATIVE STUDY OF CONTROL DESIGN FOR A CLASS OF NONLINEAR SYSTEMS USING MODIFIED STATE-DEPENDENT DIFFERENTIAL RICCATI EQUATION." OpenSIUC, 2012. https://opensiuc.lib.siu.edu/dissertations/541.
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State dependent Riccati equation (SDRE) plays an important role in nonlinear controller design. For autonomous nonlinear systems that can be expressed in linear form with state-dependent coefficients (SDC), SDRE-based controllers guarantee local asymptotic stability of the closed-loop system, under pointwise stabilizability and detectability conditions. Moreover, the optimal control for a quadratic cost function, when it exists, corresponds to an SDRE-based control design for a specific SDC parameterization of the associated nonlinear system. Unfortunately, the implementation of the SDRE-based controllers is computationally expensive. Various techniques have been developed for solving the SDRE, which are either computationally expensive or lack acceptable precision. In this dissertation, a modified state-dependent differential Riccati equation (MSDDRE) is proposed for approximating the solution of the SDRE, which is easy to implement with moderate computation power and its solution can be made arbitrarily close to that of the SDRE. Therefore, it can be used for real-time implementation of near-optimal controllers for nonlinear systems in state-dependent linear form. The proposed technique is then extended to SDRE-based filter design and its application to SDRE-based output feedback control technique. The proposed technique is also extended to state-dependent H-inf; robust control design for a constant noise attenuation bound, when the solution exists. To reduce the design conservativeness, the technique is further extended to state-dependent H-inf; robust control design with adaptive noise attenuation bound, using gain-scheduling technique and linear matrix inequality (LMI) optimization, to approximate H-inf; optimal control with state-dependent noise-attenuation bound. Local asymptotic stability of the closed-loop system is proven for all proposed techniques. Simulation results further confirm the validity of the development and demonstrate the efficiency of the proposed techniques.
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Garvie, Marcus Roland. "Analysis of a reaction-diffusion system of λ-w type." Thesis, Durham University, 2003. http://etheses.dur.ac.uk/4105/.
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The author studies two coupled reaction-diffusion equations of 'λ-w' type, on an open, bounded, convex domain Ω C R(^d) (d ≤ 3), with a boundary of class C², and homogeneous Neumann boundary conditions. The equations are close to a supercritical Hopf bifurcation in the reaction kinetics, and are model equations for oscillatory reaction-diffusion equations. Global existence, uniqueness and continuous dependence on initial data of strong and weak solutions are proved using the classical Faedo-Galerkin method of Lions and compactness arguments. The work provides a complete case study for the application of this method to systems of nonlinear reaction-diffusion equations. The author also undertook the numerical analysis of the reaction-diffusion system. Results are presented for a fully-practical piecewise linear finite element method by mimicking results in the continuous case. Semi-discrete and fully-discrete error estimates are proved after establishing a priori bounds for various norms of the approximate solutions. Finally, the theoretical results are illustrated and verified via the numerical simulation of periodic plane waves in one space dimension, and preliminary results representing target patterns and spiral solutions presented in two space dimensions.
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Tsui, Ka Cheung. "A networked PDE solving environment /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20TSUI.
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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003.Includes bibliographical references (leaves 56-58). Also available in electronic version. Access restricted to campus users.
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Luo, Ye. "Random periodic solutions of stochastic functional differential equations." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/16112.
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In this thesis, we study the existence of random periodic solutions for both nonlinear dissipative stochastic functional differential equations (SFDEs) and semilinear nondissipative SFDEs in C([-r,0],R^d). Under some sufficient conditions for the existence of global semiflows for SFDEs, by using pullback-convergence technique to SFDE, we obtain a general theorem about the existence of random periodic solutions. By applying coupled forward-backward infinite horizon integral equations method, we perform the argument of the relative compactness of Wiener-Sobolev spaces in C([0,τ],C([-r,0]L²(Ω))) and the generalized Schauder's fixed point theorem to show the existence of random periodic solutions.
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馮漢國 and Hon-kwok Fung. "Some linear preserver problems in system theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1995. http://hub.hku.hk/bib/B3121227X.
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Fung, Hon-kwok. "Some linear preserver problems in system theory /." [Hong Kong] : University of Hong Kong, 1995. http://sunzi.lib.hku.hk/hkuto/record.jsp?B16121673.
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Баранюк, Роман Андрійович. "Системи теплового захисту напівпровідникових перетворювачів електроенергії." Doctoral thesis, Київ, 2017. https://ela.kpi.ua/handle/123456789/21322.
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Дисертація присвячена розробці систем для забезпечення теплового захисту напівпровідникових перетворювачів електроенергії за рахунок суміщеного моделювання електромагнітних та теплових процесів в перетворювачах.
В роботі проведено аналіз сучасних методів розрахунку електромагнітних та теплових процесів, аналіз моделей ключових та пасивних компонентів. Показана доцільність використання моделей пасивних та активних компонентів перетворювачів параметри яких залежать від температури та електричних режимів роботи. Запропонована суміщена модель для розрахунку електротеплових процесів в перетворювачах з врахуванням швидкоплинності процесів та розділенням на системи рівнянь, що описують швидкі та повільні процеси. Запропоновані дві системи теплового захисту, які працюють за рахунок нормалізації перехідних електромагнітних процесів в колі перетворювача з врахуванням температури компонентів та перезапуску плавного пуску після зняття короткого замикання з програмним врахуванням температури компонентів.
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Hermansyah, Edy. "An investigation of collocation algorithms for solving boundary value problems system of ODEs." Thesis, University of Newcastle Upon Tyne, 2001. http://hdl.handle.net/10443/1976.
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This thesis is concerned with an investigation and evaluation of collocation algorithms for solving two-point boundary value problems for systems of ordinary differential equations. An emphasis is on developing reliable and efficient adaptive mesh selection algorithms in piecewise collocation methods. General background materials including basic concepts and descriptions of the method as well as some functional analysis tools needed in developing some error estimates are given at the beginning. A brief review of some developments in the methods to be used is provided for later referencing. By utilising the special structure of the collocation matrices, a more compact block matrix structure is introduced and an algorithm for generating and solving the matrix is proposed. Some practical aspects and computational considerations of matrices involved in the collocation process such as analysis of arithmetic operations and amount of memory spaces needed are considered. An examination of scaling process to reduce the condition number is also presented. A numerical evaluation of some error estimates developed by considering the differential operator, the related matrices and the residual is carried out. These estimates are used to develop adaptive mesh selection algorithms, in particular as a cheap criterion for terminating the computation process. Following a discussion on mesh selection strategies, a criterion function for use in adaptive algorithms is introduced and a numerical scheme to equidistributing values of the criterion function is proposed. An adaptive algorithm based on this criterion is developed and the results of numerical experiments are compared with those using some well known criterion functions. The various examples are chosen in such a way that they include problems with interior or boundary layers. In addition, an algorithm has been developed to predict the necessary number of subintervals for a given tolerance, with the aim of improving the efficiency of the whole process. Using a good initial mesh in adaptive algorithms would be expected to provide some further improvement in the algorithms. This leads to the idea of locating the layer regions and determining suitable break points in such regions before the numerical process. Based on examining the eigenvalues of the coefficient matrix in the differential equation in the specified interval, using their magnitudes and rates of change, the algorithms for predicting possible layer regions and estimating the number of break points needed in such regions are constructed. The effectiveness of these algorithms is evaluated by carrying out a number of numerical experiments. The final chapter gives some concluding remarks of the work and comment on results of numerical experiments. Certain possible improvements and extensions for further research are also briefly given.
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Siegert, Wolfgang. "Local Lyapunov exponents sublimiting growth rates of linear random differential equations." Berlin Heidelberg Springer, 2007. http://d-nb.info/991321065/04.
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McBride, Jared Adam. "Steady State Configurations of Cells Connected by Cadherin Sites." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/6023.
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Many cells employ cadherin complexes (c-sites) on the cell membrane to attach to neighboring cells, as well as integrin complexes (i-sites) to attach to a substrate in order to accomplish cell migration. This paper analyzes a model for the motion of a group of cells connected by c-sites. We begin with two cells connected by a single c-site and analyze the resultant motion of the system. We find that the system is irrotational. We present a result for reducing the number of c-sites in a system with c-sites between pairs of cells. This greatly simplifies the general system, and provides an exact solution for the motion of a system of two cells and several c-sites.Then a method for analyzing the general cell system is presented. This method involves 0-row-sum, symmetric matrices. A few results are presented as well as conjectures made that we feel will greatly simplify such analyses. The thesis concludes with the proposal of a framework for analyzing a dynamic cell system in which stochastic processes govern the attachment and detachment of c-sites.
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Yevik, Andrei. "Numerical approximations to the stationary solutions of stochastic differential equations." Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/7777.
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This thesis investigates the possibility of approximating stationary solutions of stochastic differential equations using numerical methods. We consider a particular class of stochastic differential equations, which are known to generate random dynamical systems. The existence of stochastic stationary solution is proved using global attractor approach. Euler's numerical method, applied to the stochastic differential equation, is proved to generate a discrete random dynamical system. The existence of stationary solution is proved again using global attractor approach. At last we prove that the approximate stationary point converges in mean-square sense to the exact one as the time step of the numerical scheme diminishes.
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Moreno, Claudia. "Control of partial differential equations systems of dispersive type." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASV031.
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Il existe peu de résultats dans la littérature sur la contrôlabilité du système d'équations aux dérivées partielles. Dans cette thèse, nous considérons l'étude des propriétés de contrôle pour trois systèmes couplés d'équations aux dérivées partielles de type dispersif et un problème inverse de récupération d’un coefficient. Le premier système est formé par N équations de Korteweg-de Vries sur un réseau en forme d'étoile. Pour ce système, nous étudierons la contrôlabilité exacte avec N contrôles placés aux extrémités du réseau. Le deuxième système couple trois équations de Korteweg-de Vries. Ce système est appelé dans la littérature le système Hirota-Satsuma généralisé. Nous étudions la contrôlabilité exacte avec trois contrôles frontières.Après, nous étudierons un système parabolique du quatrième ordre formé par deux équations de Kuramoto-Sivashinsky. Nous prouvons l’existence et l’unicité de la solution du système. Ensuite, nous étudions la nulle contrôlabilité du système avec deux contrôles, pour supprimer un contrôle, nous avons besoin d’une inégalité de Carleman qui n’est pas encore prouvée. Finalement, nous présentons pour le système parabolique du quatrième ordre le problème inverse de récupérer le coefficient anti-diffusion à partir des mesures de la solutionThere are few results in the literature about the controllability of partial differential equations system. In this thesis, we consider the study of control properties for three coupled systems of partial differential equations of dispersive type and an inverse problem of recovering a coefficient. The first system is formed by N Korteweg-de Vries equations on a star-shaped network. For this system we will study the exact controllability using N controls placed in the external nodes of the network. The second system couples three Korteweg-de Vries equations. This system is called in the literature the generalized Hirota-Satsuma system. We study the exact controllability with three boundary controls.On the other hand, we will study a fourth-order parabolic system formed by two Kuramoto-Sivashinsky equations. We prove the well-posedness of the system with some regularity results. Then we study the null controllability of the system with two controls, to remove a control, we need a Carleman inequality which is not proven yet. Finally, we present for the fourth-order parabolic system the inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution
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Post, Katharina. "A System of Non-linear Partial Differential Equations Modeling Chemotaxis with Sensitivity Functions." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 1999. http://dx.doi.org/10.18452/14365.
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Wir betrachten ein System nichtlinearer parabolischer partieller Differentialgleichungen zur Modellierung des biologischen Phänomens Chemotaxis, das unter anderem in Aggregationsprozessen in Lebenszyklen bestimmter Einzeller eine wichtige Rolle spielt. Unser Chemotaxismodell benutzt Sensitivitäts funktionen, die die vorkommenden biologischen Prozesse genauer spezifizieren. Trotz der durch die Sensitivitätsfunktionen eingebrachten, zusätzlichen Nichtlinearitäten in den Gleichungen erhalten wir zeitlich globale Existenz von Lösungen für verschiedene biologisch realistische Klassen von Sensitivitätsfunktionen und können unter unterschiedlichen Bedingungen an die Systemdaten Konvergenz der Lösungen zu trivialen und nicht-trivialen stationären Punkten beweisen.We consider a system of non-linear parabolic partial differential equations modeling chemotaxis, a biological phenomenon which plays a crucial role in aggregation processes in the life cycle of certain unicellular organisms. Our chemotaxis model introduces sensitivity functions which help describe the biological processes more accurately. In spite of the additional non-linearities introduced by the sensitivity functions into the equations, we obtain global existence of solutions for different classes of biologically realistic sensitivity functions and can prove convergence of the solutions to trivial and non-trivial steady states.
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Shikongo, Albert. "Robust numerical methods to solve differential equations arising in cancer modeling." University of the Western Cape, 2020. http://hdl.handle.net/11394/7250.
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Philosophiae Doctor - PhDCancer is a complex disease that involves a sequence of gene-environment interactions in a progressive process that cannot occur without dysfunction in multiple systems. From a mathematical point of view, the sequence of gene-environment interactions often leads to mathematical models which are hard to solve analytically. Therefore, this thesis focuses on the design and implementation of reliable numerical methods for nonlinear, first order delay differential equations, second order non-linear time-dependent parabolic partial (integro) differential problems and optimal control problems arising in cancer modeling. The development of cancer modeling is necessitated by the lack of reliable numerical methods, to solve the models arising in the dynamics of this dreadful disease. Our focus is on chemotherapy, biological stoichometry, double infections, micro-environment, vascular and angiogenic signalling dynamics. Therefore, because the existing standard numerical methods fail to capture the solution due to the behaviors of the underlying dynamics. Analysis of the qualitative features of the models with mathematical tools gives clear qualitative descriptions of the dynamics of models which gives a deeper insight of the problems. Hence, enabling us to derive robust numerical methods to solve such models.
2021-04-30
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Whitaker, Shree Yvonne. "A Biologically-Based Controlled Growth and Differentiation Model Using Delay Differential Equations: Development, Applications and Stability Analysis." NCSU, 2000. http://www.lib.ncsu.edu/theses/available/etd-20001120-152601.
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This work investigates the development, applications and stability analysis of a biologically-based dose-response model for developmental toxicology. The biologically-based controlled growth and differentiation model is based on a model originally developed by Leroux et al. (1996). The original model had two basic states; precursor cells and differentiated cells with both states subject to a linear birth-death process. The research discussed in this dissertation describes the development of a mathematical model that is both biologically- and statistically-based. The model is developed with a highly controlled birth and death process for precursor cells. This model limits the number of replications allowed in the development of a tissue or organ and more closely reflects the presence of a true stem cell population. The mathematical formulation of the Leroux et al. (1996) model was derived from a partial differential equation for the generating function that limits further expansion into more realistic models of mammalian development. The same formulae for the probability of a defect (a system of ordinary differential equations) can be derived through the Kolmogorov forward equations due to the nature of this Markov process. This modified approach is easily amenable to the expansion of more complicated models of the developmental process. Comparisons between the Leroux et al. (1996) model and the controlled growth and differentiation (CGD) model are also discussed.The versatility of the CGD model is highlighted through a discussion of two general applications. The normal developmental process of spermatocytogenesis is investigated as the first application. Time delays are introduced into the system to more accurately mimic the development of male germ cells. As the second application, the spermatocytogenesis model is then altered to demonstrate a modeling strategy for hormesis. Asymptotic stability is investigated using the system of delay differential equations for spermatocytogenesis. The direct Lyapunov method for linear differential equations without delay is modified to establish delay-dependent stability conditions for delay differential equations with multiple delays. The stability conditions are expressed in terms of the existence of a positive definite solution to the Riccati matrix equations. Numerical simulations further verify the stability conditions.
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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 condition is investigated in chapter 3. In chapter4, we give a result that characterizes the behavior of solutions in the case there is a bounded solution. Moreover, a necessary and sufficient condition for the existence of periodic solutions is obtained. In the last chapter, a series of consequences on the existence of periodic solutions of functionally equivlent impulsive systems with delays is established.
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Barwani, Rahima. "Stoke's multipliers for a certain third order differential equation near an irregular singular point." Virtual Press, 1986. http://liblink.bsu.edu/uhtbin/catkey/454815.
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This thesis is concerned with the asymptotic solutions of the differential equationz(2) d(3)y/dz(3) + (a0z) d(2)y/dz(2) + [b0+b1z+b2z(2)] dy/dz + (c0+ c1z) y=0Here, the variable z is complex as are the constants ai, ci(i=O,1) and bi(i=O,1,2) with b2 does not equal 0. It is also assumed that the roots of the indicial equation about z = 0 are such that the difference of no two of them is congruent to zero modular 1.Ball State UniversityMuncie, IN 47306