Relevant bibliographies by topics / Centre manifold theory / Dissertations / Theses
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Dissertations / Theses on the topic 'Centre manifold theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 January 2023

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1

Liu, Weishi. "Center manifold theory for smooth invariant manifolds." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/28762.

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2

Allahem, Ali Ibraheem. "Numerical investigation of chaotic dynamics in multidimensional transition states." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/14058.

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Many chemical reactions can be described as the crossing of an energetic barrier. This process is mediated by an invariant object in phase space. One can construct a normally hyperbolic invariant manifold (NHIM) of the reactive dynamical system which is an invariant sphere that can be considered as the geometric representation of the transition state itself. The NHIM has invariant cylinders (reaction channels) attached to it. This invariant geometric structure survives as long as the invariant sphere is normally hyperbolic. We applied this theory to the hydrogen exchange reaction in three degr
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3

MacKenzie, Tony. "Create accurate numerical models of complex spatio-temporal dynamical systems with holistic discretisation." University of Southern Queensland, Faculty of Sciences, 2005. http://eprints.usq.edu.au/archive/00001466/.

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This dissertation focuses on the further development of creating accurate numerical models of complex dynamical systems using the holistic discretisation technique [Roberts, Appl. Num. Model., 37:371-396, 2001]. I extend the application from second to fourth order systems and from only one spatial dimension in all previous work to two dimensions (2D). We see that the holistic technique provides useful and accurate numerical discretisations on coarse grids. We explore techniques to model the evolution of spatial patterns governed by pdes such as the Kuramoto-Sivashinsky equation and the real-va
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4

Lichtner, Mark. "Exponential dichotomy and smooth invariant center manifolds for semilinear hyperbolic systems." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=981306659.

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5

Silva, Vinicius Barros da. "Bifurcação de Hopf e formas normais : uma nova abordagem para sistemas dinâmicos /." Rio Claro, 2018. http://hdl.handle.net/11449/180496.

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Orientador: Edson Denis Leonel<br>Resumo: Este estudo objetiva provar que sistemas dinâmicos de dimensão N, de codimensão um e satisfazendo as condições do teorema da bifurcação de Hopf, podem ser expressos em uma forma analítica simplificada que preserva a topologia do espaço de fases da configuração original, na vizinhança do ponto de equilíbrio. A esta forma simplificada é atribuído o nome de forma normal. Para tanto, foi utilizado a teoria da variedade central, necessária para reduzir a dimensão de sistemas à sua variedade bidimensional, e o teorema das formas normais, utilizando-se como m
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6

Kasnakoglu, Cosku. "Reduced order modeling, nonlinear analysis and control methods for flow control problems." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1195629380.

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7

Arugaslan, Cincin Duygu. "Differential Equations With Discontinuities And Population Dynamics." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12610574/index.pdf.

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In this thesis, both theoretical and application oriented results are obtained for differential equations with discontinuities of different types: impulsive differential equations, differential equations with piecewise constant argument of generalized type and differential equations with discontinuous right-hand sides. Several qualitative problems such as stability, Hopf bifurcation, center manifold reduction, permanence and persistence are addressed for these equations and also for Lotka-Volterra predator-prey models with variable time of impulses, ratio-dependent predator-prey systems and lo
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8

Marmo, Carlos Nehemy. "Bifurcações em PLLs de terceira ordem em redes OWMS." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/3/3139/tde-29012009-103841/.

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Este trabalho apresenta um estudo qualitativo das equações diferenciais nãolineares que descrevem o sincronismo de fase nos PLLs de 3ª ordem que compõem redes OWMS de topologia mista, Estrela Simples e Cadeia Simples. O objetivo é determinar, através da Teoria de Bifurcações, os valores ou relações entre os parâmetros constitutivos da rede que permitam a existência e a estabilidade do estado síncrono, quando são aplicadas, no oscilador mestre, duas funções de excitação muito comuns na prática: o degrau e a rampa de fase. Na determinação da estabilidade dos pontos de equilíbrio, sob o ponto de
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9

Garcia, Ignacio de Mateo. "Iterative matrix-free computation of Hopf bifurcations as Neimark-Sacker points of fixed point iterations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2012. http://dx.doi.org/10.18452/16478.

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Klassische Methoden für die direkte Berechnung von Hopf Punkten und andere Singularitaten basieren auf der Auswertung und Faktorisierung der Jakobimatrix. Dieses stellt ein Hindernis dar, wenn die Dimensionen des zugrundeliegenden Problems gross genug ist, was oft bei Partiellen Diferentialgleichungen der Fall ist. Die betrachteten Systeme haben die allgemeine Darstellung f ( x(t), α) für t grösser als 0, wobei x die Zustandsvariable, α ein beliebiger Parameter ist und f glatt in Bezug auf x und α ist. In der vorliegenden Arbeit wird ein Matrixfreies Schema entwicklet und untersucht, dass
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10

Marmo, Carlos Nehemy. "Sincronismo em redes mestre-escravo de via-única: estrela simples, cadeia simples e mista." Universidade de São Paulo, 2003. http://www.teses.usp.br/teses/disponiveis/3/3139/tde-18022004-233234/.

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Neste trabalho, são estudados os problemas de sincronismo de fase nas redes mestre-escravo de via única (OWMS), nas topologias Estrela Simples, Cadeia Simples e mista, através da Teoria Qualitativa de Equações Diferenciais, com ênfase no Teorema da Variedade Central. Através da Teoria das Bifurcações, analisa-se o comportamento dinâmico das malhas de sincronismo de fase (PLL) de segunda ordem que compõem cada rede, frente às variações nos seus parâmetros constitutivos. São utilizadas duas funções de excitação muito comuns na prática: o degrau e a rampa de fase, aplicadas pelo nó mestre. Em cad
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11

Phongi, Eddy Kimba. "Centre manifold theory with an application in population modelling." Thesis, 2009. http://hdl.handle.net/10413/431.

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There are basically two types of variables in population modelling, global and local variables. The former describes the behavior of the entire population while the latter describes the behavior of individuals within this population. The description of the population using local variables is more detailed, but it is also computationally costly. In many cases to study the dynamics of this population, it is sufficient to focus only on global variables. In applied sciences, to achieve this, the method of aggregation of variables is used. One of methods used to mathematically justify variables agg
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12

Chen, Chen. "Multiscale modelling of continuum and discrete dynamics in materials with complicated microstructure." Thesis, 2015. http://hdl.handle.net/2440/98116.

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Homogenization and other multiscale modelling techniques empower scientist and engineers to build efficient macroscale mathematical models for simulating materials with complicated microstructure. But the modelling methodology rarely systematically derives the boundary conditions for macroscale model. This thesis aims to systematically derive boundary conditions for macroscale models without heuristic arguments. I start by building a smooth macroscale model for a one-dimensional discrete diffusion system with rapidly varying microscale diffusivity, finite scale separation, and Dirichlet bounda
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13

Podder, Chandra Nath. "Mathematics of HSV-2 Dynamics." 2010. http://hdl.handle.net/1993/4082.

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The thesis is based on using dynamical systems theories and techniques to study the qualitative dynamics of herpes simplex virus type 2 (HSV-2), a sexually-transmitted disease of major public health significance. A deterministic model for the interaction of the virus with the immune system in the body of an infected individual (in vivo) is designed first of all. It is shown, using Lyapunov function and LaSalle's Invariance Principle, that the virus-free equilibrium of the model is globally-asymptotically stable whenever a certain biological threshold, known as the reproduction number, is l
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14

Chaudhary, Osman. "Rigorous justification of Taylor Dispersion via Center Manifold theory." Thesis, 2017. https://hdl.handle.net/2144/24106.

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Imagine fluid moving through a long pipe or channel, and we inject dye or solute into this pipe. What happens to the dye concentration after a long time? Initially, the dye just moves along downstream with the fluid. However, it is also slowly diffusing down the pipe and towards the edges as well. It turns out that after a long time, the combined effect of transport via the fluid and this slow diffusion results in what is effectively a much more rapid diffusion process, lengthwise down the stream. If 0 <nu << 1 is the slow diffusion coeffcient, then the effective longitudinal diffusion
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15

Nazari, Fereshteh. "Backward bifurcation in HCV transmission dynamics." 2014. http://hdl.handle.net/1993/23821.

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The thesis is based on the use of mathematical theories and techniques to gain qualitative and quantitative insight into the transmission dynamics of hepatitis C virus (HCV) in an IDU (injecting drug user) population. A deterministic model, which stratifies the IDU population into eight mutually-exclusive compartments (based on epidemiological status), is considered. Rigorous qualitative analysis of the model establishes, for the first time, the presence of the phenomenon of backward bifurcation in HCV transmission dynamics. Three routes (or causes) to such a dynamic phenomenon have been estab
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16

"Analysis and Control of Space Systems Dynamics via Floquet Theory, Normal Forms and Center Manifold Reduction." Doctoral diss., 2019. http://hdl.handle.net/2286/R.I.55623.

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abstract: It remains unquestionable that space-based technology is an indispensable component of modern daily lives. Success or failure of space missions is largely contingent upon the complex system analysis and design methodologies exerted in converting the initial idea into an elaborate functioning enterprise. It is for this reason that this dissertation seeks to contribute towards the search for simpler, efficacious and more reliable methodologies and tools that accurately model and analyze space systems dynamics. Inopportunely, despite the inimical physical hazards, space systems must en
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17

Δερμιτζάκης, Ιωάννης. "Βελτιστοποίηση διεργασιών υπό περιοδική λειτουργία". Thesis, 2009. http://nemertes.lis.upatras.gr/jspui/handle/10889/1776.

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Το Πι-κριτήριο των Bittanti et al. (1973) έχει χρησιμοποιηθεί εκτενώς σε εφαρμογές με στόχο την πρόβλεψη ενδεχόμενης βελτίωσης της απόδοσης ενός μη γραμμικού συστήματος υπό περιοδική είσοδο. Το κριτήριο όμως έχει τοπική ισχύ και περιορίζεται σε περιοδικές διαταραχές μικρού πλάτους. Η παρούσα εργασία αναπτύσσει μια μέθοδο προσδιορισμού διορθώσεων υψηλότερης τάξης στο πι-κριτήριο, προερχόμενη από βασικά αποτελέσματα της θεωρίας κεντρικής πολλαπλότητας (Center Manifold theory). Η προτεινόμενη μέθοδος βασίζεται στην επίλυση της μερικής διαφορικής εξίσωσης της κεντρικής πολλαπλότητας με χρήση δυναμ
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