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Dissertations / Theses on the topic 'Nonlinear dynamics'
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Shin, Hyunkyoung. "Nonlinear cable dynamics." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/14647.
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Kenwright, David A. "Nonlinear dynamics of anaesthesia." Thesis, Lancaster University, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.538583.
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Chin, Char-Ming. "Problems in nonlinear dynamics." Diss., This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06062008-165621/.
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Shekhawat, Ashivni. "Nonlinear dynamics of hysteretic oscillators." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-2856.
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Liu, Xunmimg. "Nonlinear dynamics in quantum optics /." St. Lucia, Qld, 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17835.pdf.
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Tsukamoto, Naofumi. "Phase dynamics in nonlinear systems." 京都大学 (Kyoto University), 2008. http://hdl.handle.net/2433/136010.
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Manzan, Sebastiano. "Essays in nonlinear economic dynamics." [Amsterdam : Amsterdam : Thela Thesis] ; Universiteit van Amsterdam [Host], 2003. http://dare.uva.nl/document/68437.
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Pointon, Craig T. "Nonlinear dynamics in telecommunication systems." Thesis, Staffordshire University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282553.
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Stocks, Nigel Geoffrey. "Experiments in stochastic nonlinear dynamics." Thesis, Lancaster University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315224.
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Shiogai, Yuri. "Nonlinear dynamics of cardiovascular aging." Thesis, Lancaster University, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444859.
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Maksymczuk, J. "Nonlinear equilibration of fast dynamics." Thesis, University of Essex, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302631.
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Lu, Weiping. "Nonlinear dynamics of optical systems." Thesis, Heriot-Watt University, 1991. http://hdl.handle.net/10399/836.
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Kapitaniak, Marcin. "Nonlinear dynamics of drill-strings." Thesis, University of Aberdeen, 2015. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=227960.
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This thesis has been motivated by the need to construct reliable, experimentally callibrated models of the drill-string assembly, that capture important phenomena associated with the drilling process, such as torsional oscillations, stick-slip and whirling. This can be achieved using a continuous finite element model, as well as low-dimensional torsional pendulum models in limited cases. The importance of this work lies in the fact, that the experimental rig utilizes real industrial drillbits and rock samples, which after careful identification of TOB speed curves, allows to use an equivalent friction model to accommodate for both frictional and cutting components of the bit-rock interactions. As a first step, a preliminary calibration of the FE model for a straight configuration of the drill-string is carried out, that allows to utilize the low-dimensional model to replicate behaviour of the system. In both of these cases, the agreement between experiments and modelling is achieved. Based on these preliminary studies, it is possible to verify the model in a prebuckled drill-string configuration, for which case a qualitative as well as quantitative agreement with the experiment is obtained. This allows to identify regions where the most dangerous phenomenon of stick-slip is present in parameter space of WOB and top angular speed. Next, the analysis is focused on the whirling phenomenon and calibration of the reduced order rotor model to replicate the motion of the BHA in the bore-hole. A qualitative agreement with the experiments is obtained. An interesting phenomenon of co-existing forward and backward periodic whirling solutions are observed both experimentally and numerically. The influence of the initial conditions and the friction between the BHA and the borehole are investigated, what revealed that there is a threshold value of friction coefficient for which the whirling direction changes from forward to backward.
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Nayfeh, Mahir Ali. "Nonlinear dynamics in power systems." Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/41582.
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We use a perturbation analysis to predict some of the instabilities in a single-machine quasi-infinite busbar system. The system’s behavior is described by the so-called swing equation, which is a nonlinear second-order ordinary-differential equation with additive and multiplicative harmonic terms having the frequency Ω. When Ω≈ω₀, and Ω≈2ω₀, where ω₀ is the linear natural frequency of the machine, we use digital-computer simulations to exhibit some of the complicated responses of the machine, including period-doubling bifurcations, chaotic motions, and unbounded motions (loss of synchronism). To predict the onset of these complicated behaviors, we use the method of multiple scales to develop approximate closed-form expressions for the periodic responses of the machine. Then, we use various techniques to determine the stability of the analytical solutions. The analytically predicted periodic solutions and conditions for their instability are in good agreement with the digital-computer results.Master of Science
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Mudd, Tom. "Nonlinear dynamics in musical interactions." Thesis, Open University, 2017. http://oro.open.ac.uk/52231/.
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This thesis examines nonlinear dynamical processes in musical tools, identifying certain roles that they play in creative interactions with existing tools, and investigates the roles they might play in digital tools. Nonlinear dynamical processes are fundamental in the everyday physical world. They lie at the core of many acoustic instruments, playing a particularly significant role in bowed and blown instruments. Two major studies are presented that approach these issues from different perspectives. Firstly a set of comparative studies explore the ways in which musicians engage with systems that do and do not incorporate nonlinear dynamical processes. Secondly, interviews with a range of musicians engaged in contemporary musical practices — particularly free improvisation — are used to investigate the role of nonlinear dynamical processes in instrumental interactions in relation to unpredictability and creative exploration. Evidence is presented demonstrating that nonlinear dynamical processes can be drawn on as resources for exploration over long time periods. An approach to creative interaction that explicitly draws on the properties of nonlinear dynamical processes is uncovered and connected to material-oriented notions of creative processes. Nonlinear dynamics are shown to facilitate a productive ‘‘sweet spot’’ between unpredictability and complexity on the one hand, and detailed, sensitive, deterministic control, coupled with the potential to repeat and develop particular actions on the other. The importance of timing in interactions with nonlinear dynamical processes is highlighted as being significant in creating explorable interactions, particularly close to critical thresholds. A distinction is raised between instantaneous unpredictabilities that emerge from the interaction with the tool (interactional ), and unpredictabilities that result from the unexpected implications of the conjunction of otherwise anticipated elements (combinatorial). While the usefulness of the latter in creative interactions is frequently acknowledged in HCI research, the former is often excluded, or seen as a hinderance or obstruction. Engagements with nonlinear dynamical processes in existing musical instruments and practices provide clear evidence of the utility of both nonlinear dynamics, and interactional surprises more generally, suggesting that they can be of use in other domains where creative exploration is a concern.
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Scott, Andrew J. "Classical and quantum nonlinear dynamics /." [St. Lucia, Qld.], 2001. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe16384.pdf.
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Neubauer, Jürgen. "Nonlinear dynamics of the voice." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2005. http://dx.doi.org/10.18452/15343.
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Die Physik der Lauterzeugung (Phonation) wurde mit Hilfe der Theorie der Nichtlinearen Dynamik untersucht. Digitale Hochgeschwindigkeitsaufnamen von Schwingungen in menschlichen und nichtmenschlichen Kehlkoepfen, digitale Bildanalyse, Signalanalyse und Modenanalyse wurden zur quantitativen Beschreibung nichtlinearer Phaenomene eingesetzt. Es wurden nichtlineare Phaenomene bei stimmkranker (pathologischer) menschlicher Lauterzeugung untersucht, wie auch in stimmgesunden Singstimmen und in Kehlkoepfen von nichtmenschlichen Saeugetieren mit Stimmlippen-Membranen. Durch Bifurkationsanalyse eines einfachen mathematischen Modells fuer Stimmlippen mit Membranen konnten beobachtete Lautmuster nichtmenschlicher Saeugetiere qualitativ "nichtlinear gefittet" werden. Die Schwerpunkte dieser Arbeit waren: 1. die Klassifikation von Lautmustern in zeitgenoessischer Vokalmusik, um Erzeugungsmechanismen fuer komplexe Stimmklaenge zu erklaeren, die im kuenstlerischen Kontext vorkommen. Im besonderen war die Rolle der Quelle-Trakt-Kopplung von Interesse; 2. Instabilitaeten in Stimmpatienten, die durch Asymmetrien in einzelnen Stimmlippen wie auch zwischen den Stimmlippen verursacht wurden; 3. dynamische Effekte von duennen, leichten und schwingenden Stimmlippen-Membranen, vertikalen Fortsaetzen der Stimmlippen bei Saeugetieren. Stimmlippen-Membrane finden sich in Kehlkoepfen von Fledermaeusen und Primaten, wo sie einerseits zur Ultraschallerzeugung verwendet werden und andererseits fuer eine grosse Lautvielfalt sorgen. Ein Stimmlippen-Membran-Modell wurde entwickelt, um dieses diverse Lautrepertoire zu reproduzieren. Dieses Modell zeigte zwei Stimmregister. Ueber die Geometry der Stimmlippen-Membrane konnte der subglottale Einsatzdruck minimiert werden und der Druckbereich fuer Phonationen vergroessert werden. Numerische Simulationen demonstrierten, dass das phaenomenologische Stimm-Membran-Modell das Lautrepertoire von Fledermaeusen und Primaten qualitativ reproduzieren konnte.In this thesis, the physics of phonation was discussed using the theory of nonlinear dynamics. Digital high speed recordings of human and nonhuman laryneal oscillations, image processing, signal analysis, and modal analysis have been used to quantitatively describe nonlinear phenomena in pathological human phonation, healthy voices in singing, and nonhuman mammalian larynges with vocal membranes. Bifurcation analysis of a simple mathematical model for vocal folds with vocal membranes allowed a qualitative ''nonlinear fit'' of observed vocalization patterns in nonhuman mammals. The main focus of the present work was on: 1. the classification of vocalizations of contemporary vocal music to provide insight to production mechanisms of complex sonorities in artistic contexts, especially to nonlinear source-tract coupling; 2. pathological voice instabilities induced by asymmetries within single vocal folds and between vocal folds; 3. the dynamic effects of thin, lightweight, and vibrating vocal membranes as upward extensions of vocal folds in nonhuman mammals. In nonhuman mammals, vocal membranes are one widespread morphological variation of vocal folds. In bats they are responsible to produce ultrasonic echolocation calls. In nonhuman primates they facilitate the production of highly diverse vocalizations. A vocal membrane model was developed to understand the production of these complex calls. Two voice registers were found in the vocal membrane model. The vocal membrane geometry could minimize phonation onset pressure and enlarge the phonatory pressure range of the model. Numerical simulations of the model revealed instabilities that qualitatively resembled observed vocalization patterns in bats and primates.
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Schumann, Michael. "Nonlinear dynamics in oscillating waterfalls." PDXScholar, 1992. https://pdxscholar.library.pdx.edu/open_access_etds/4421.
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Johnson, Holly. "Nonlinear dynamics of wake vortices." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX101/document.
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Les tourbillons de sillage d’avion sont sources de problèmes économiques, environnementaux et de sécurité, et par conséquent ont fait l’objet de très nombreuses recherches depuis plusieurs dizaines d’années. Le sillage est composé d’une paire de tourbillons contrarotatifs qui perdurent longtemps après le passage de l’avion. Dans cette thèse la dynamique non linéaire de ces tourbillons desillage est examinée par Simulation Numérique Directe. L’objectif est d’étudier les comportements non linéaires des tourbillons de sillage et d’évaluer le potentiel de destruction anticipée des tourbillons par la perturbation optimale. Dans un premier temps, le potentiel destructeur de la perturbation optimale linéaire est estimé en l’appliquant aux tourbillons avec une amplitude initiale croissante et en observant la réponse non linéaire de l’écoulement. Une amplitude raisonnable suffit pour que la perturbation optimale linéaire réduise de moitié la durée de vie des tourbillons en accélérant une perte de cohérence des structures après l’étape de reconnexion. Par la suite, l’outil d’optimisation non linéaire développé au cours de la thèse est validé par la reproduction de résultats existants concernant un écoulement simple: un toubillon 2D isolé. De nouveaux résultats d’optimisation non linéaire sont obtenus et analysés. En particulier, la perturbation optimale non linéaire 2D d’un tourbillon isolé peut générer une croissance transitoire bien plus élevée que la perturbation optimale linéaire. Dans certains cas la perturbation optimale non linéaire provoque une transition vers un état non axisymétrique quasi-stationnaire,contournant ainsi le processus naturel d’axisymétrisation. De plus, l’effet de la distribution de vorticité dans le coeur du tourbillon sur les perturbations optimales est étudié. Les tourbillons ayant un profil plus raide que les tourbillons Gaussiens subissent une croissance transitoire linéaire plus élevée mais une croissance non linéaire plus faible. Enfin, l’analyse de perturbation optimale non linéaire est étendue aux perturbations 3D. Bien que les perturbations optimales non linéaires 3D produisent moins d’amplification, des transitions vers des états énergétiques et persistants sont observéesAircraft wakes have been the subject of extensive research for several decades as it poses economic, safety and environmental issues. The wake is composed of powerful counter-rotating vortices that persist long after the aircraft has passed. In this thesis, the nonlinear dynamics of aircraft wake vortices is investigated through Direct Numerical Simulation. The aim is to explore the nonlinear effects on wake vortex behaviour and evaluate the potential for the anticipated destruction of the vortices through optimal perturbation. First the disruptive potential of the linear optimal perturbation of the flow is evaluated by applying it with increasing initial amplitude and observing the nonlinear response of the flow. With sufficient yet reasonable initial amplitude the linear optimal perturbation halves the life-span of the vortex pair by accelerating the loss of coherence of the vortices after the linking phase. Next the nonlinear gradient-based optimisation tool that was developed during the thesis is validated by reproducing existing results concerning a simple vortical flow: an isolated two-dimensional vortex. In doing so new nonlinear optimisation results are obtained and analysed. In particular it is shown that the 2D nonlinear optimal perturbation of an isolated vortex can induce considerably greater transient growth than the linear optimal. In some cases the nonlinear optimal causes a transition to a quasisteady asymmetric state, bypassing the natural axisymmetrisation process. The effect of the vortex vorticity profile on the optimal perturbations is also studied. Vortices with sharper profiles experiencefar greater linear perturbation growth, however the nonlinear growth is significantly inferior. Finally the nonlinear optimal perturbation analysis of the isolated vortex is extended to three dimensions. Although the 3D nonlinear optimals produce less growth than their linear counterparts, they can lead to quasi-permanent high energy states
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Ruzziconi, Laura. "Nonlinear dynamics in microelectromechanical systems." Doctoral thesis, Università Politecnica delle Marche, 2011. http://hdl.handle.net/11566/242133.
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La tesi affronta lo studio delle dinamiche nonlineari in alcuni dispositivi MEMS. Le tematiche di dinamica nonlineare attualmente affrontate in letteratura sono indispensabili per studiare la
loro risposta. L’accuratezza della modellazione dinamica nonlineare è importante per garantire l’affidabilità dei risultati e gli strumenti attuali di dinamica nonlineare riescono ad
interpretare scrupolosamente i dati sperimentali della risposta di questi dispositivi. La tesi considera due diversi casi-studio. Il primo caso-studio è un dispositivo MEMS con carico assiale, forma iniziale ad arco molto ribassato e attuazione elettrostatica ed elettrodinamica. È analizzato in un intorno della biforcazione da una singola ad una doppia buca di potenziale. Sia le configurazioni statiche nonlineari sia l’analisi dinamica lineare non possono essere risolte in forma chiusa e sono
approssimate con il metodo di Galerkin. Vengono usate per costruire un accurato modello ridotto delle dinamiche nonlineari ad un solo grado di libertà. In questo modello il termine del quinto ordine (che dipende dall’espansione in serie di Taylor nell’equazione del moto) è eliminato per avere una buona approssimazione delle buche di potenziale e del comportamento globale. Altri modelli ridotti sono considerati e paragonati. Si esegue l’analisi
dinamica nonlineare, con l’uso combinato di curve di risposta in frequenza, ritratti di fase attrattori-bacini e mappe di comportamento. In un intorno di ciascuna frequenza naturale, la risposta del dispositivo presenta le tipiche caratteristiche di un oscillatore softening. I casi di singola e doppia buca di potenziale vengono paragonati.
Il secondo caso-studio analizza i dati sperimentali di pull-in dinamico in risonanza primaria di
un dispositivo MEMS (un accelerometro capacitivo). Iniziando da questo caso particolare, si affronta la tematica dell’integrità dinamica in un sistema meccanico. Viene eseguito il suo
calcolo qualitativo, scegliendo gli strumenti più appropriati in base alle condizioni sperimentali considerate. Si evidenzia l’efficacia di questa analisi, mostrando l’accuratezza delle curve di percentuale costante di fattore di integrità nell’interpretare l’esistenza di
disturbi negli esperimenti e nella pratica. Inoltre, si mostra il loro utilizzo nella progettazione.This dissertation deals with the nonlinear dynamics in MEMS devices. The nonlinear dynamic topics currently addressed in the literature are essential to investigate their response. The accuracy of the nonlinear dynamic modeling is important to guarantee the reliability of the results and current nonlinear dynamic tools succeed in carefully interpreting the experimental data of the response of these devices. The dissertation considers two different case-studies. The first case-study is a MEMS device with axial load, very shallow arched initial shape and electrostatic and electrodynamic actuation. It is analyzed in the neighborhood of the bifurcation from a single potential well to a twin well. Both the nonlinear static configurations and the linear dynamic analysis cannot be solved in closed form and they are approximated by the Galerkin technique. They are used to derive an accurate single degree of freedom reduced order model of the nonlinear dynamics. In this model the fifth order term (connected to the Taylor expansion in the equation of motion) is removed to obtain a good approximation of the potential wells and of the global behavior. Other reduced order models are considered and compared. The nonlinear dynamic analysis is performed, with the combined use of frequency response curves, attractor-basins phase portraits and behavior charts. In a neighborhood of each natural frequency, the response of the device has the typical characteristics of a softening oscillator. The cases of the single and the double potential well are compared. The second case-study analyzes the experimental dynamic pull-in data at primary resonance for a MEMS device (a capacitive accelerometer). Starting from this particular case, the issue of the dynamical integrity in a mechanical system is addressed. Its qualitative evaluation is performed, choosing the most suitable tools according to the considered experimental conditions. The effectiveness of this analysis is highlighted, showing the accuracy of the curves of constant percentage of integrity factor in interpreting the existence of disturbances in experiments and practice. Also, their use in a design is proposed.
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Wu, Ye. "Nonlinear dynamics in complex networks and modeling human dynamics." Phd thesis, Universität Potsdam, 2010. http://opus.kobv.de/ubp/volltexte/2010/4735/.
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Durch große Datenmengen können die Forscher die Eigenschaften komplexer Systeme untersuchen, z.B. komplexe Netzwerk und die Dynamik des menschlichen Verhaltens. Eine große Anzahl an Systemen werden als große und komplexe Netzwerke dargestellt, z.B. das Internet, Stromnetze, Wirtschaftssysteme. Immer mehr Forscher haben großes Interesse an der Dynamik des komplexen Netzwerks.
Diese Arbeit besteht aus den folgenden drei Teilen. Der erste Teil ist ein einfacher dynamischer Optimierungs-Kopplungs-Mechanismus, aber sehr wirksam. Durch den Mechanismus kann synchronisation in komplexen Netzwerken mit und ohne Zeitverzögerung realisiert, und die Fähigkeit der Synchronisation von small-world und scale-free Netze verbessert werden.
Im zweiten Teil geht um die Verstärkung der Robustheit der scale-free Netze im Zusammenhang mit der Gemeinden-Struktur. Einige Reaktionsmuster und topologische Gemeinden sind einheitlich. Die Ergebnisse zeigen einen neuen Aspekt der Beziehung zwischen den Funktionen und der Netzwerk-Topologie von komplexen Netzwerken.
Im dritten Teil welche eine wichtige Rolle in komplexen Netzwerken spielt, wird die Verhaltens-Dynamik der menschliche Mitteilung durch Daten- und Modellanalysierung erforscht, dann entsteht ein neues Mitteilungsmodell. Mit Hilfe von einem Interaktion priority-Queue Model kann das neue Modell erklärt werden. Mit Hilfe des Models können viele praktische Interaktions-Systeme erklärt werden, z.B. E-Mail und Briefe (oder Post). Mit Hilfe meiner Untersuchung kann man menschliches Verhalten auf der Individuums- und Netzwerkebene neu kennenlernen.
Im vierter Teil kann ich nachweisen, dass menschliches Kommentar-Verhalten in on-line Sozialsystemen, eine andere Art der Interaktionsdynamik von Mensch non-Poisson ist und dieses am Modell erklären. Mit Hilfe der non-Poisson Prozesse kann man das persönliche Anziehungskraft-Modell besser verstehen. Die Ergebnisse sind hilfreich zum Kennenlernen des Musters des menschlichen Verhaltens in on-line Gesellschaften und der Entwicklung von öffentlicher Meinung nicht nur in der virtuellen Gesellschaftn sondern auch in der Realgesellschaft.
Am Ende geht es um eine Prognose von menschlicher Dynamik und komplexen Netzwerken.The availability of large data sets has allowed researchers to uncover complex properties in complex systems, such as complex networks and human dynamics. A vast number of systems, from the Internet to the brain, power grids, ecosystems, can be represented as large complex networks. Dynamics on and of complex networks has attracted more and more researchers’ interest. In this thesis, first, I introduced a simple but effective dynamical optimization coupling scheme which can realize complete synchronization in networks with undelayed and delayed couplings and enhance the small-world and scale-free networks’ synchronizability. Second, I showed that the robustness of scale-free networks with community structure was enhanced due to the existence of communities in the networks and some of the response patterns were found to coincide with topological communities. My results provide insights into the relationship between network topology and the functional organization in complex networks from another viewpoint. Third, as an important kind of nodes of complex networks, human detailed correspondence dynamics was studied by both data and the model. A new and general type of human correspondence pattern was found and an interacting priority-queues model was introduced to explain it. The model can also embrace a range of realistic social interacting systems such as email and letter communication. My findings provide insight into various human activities both at the individual and network level. Fourth, I present clearly new evidence that human comment behavior in on-line social systems, a different type of interacting human dynamics, is non-Poissonian and a model based on the personal attraction was introduced to explain it. These results are helpful for discovering regular patterns of human behavior in on-line society and the evolution of the public opinion on the virtual as well as real society. Finally, there are conclusion and outlook of human dynamics and complex networks.
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Marsden, Christopher J. "Nonlinear dynamics of pattern recognition and optimization." Thesis, Loughborough University, 2012. https://dspace.lboro.ac.uk/2134/10694.
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We associate learning in living systems with the shaping of the velocity vector field of a dynamical system in response to external, generally random, stimuli. We consider various approaches to implement a system that is able to adapt the whole vector field, rather than just parts of it - a drawback of the most common current learning systems: artificial neural networks. This leads us to propose the mathematical concept of self-shaping dynamical systems. To begin, there is an empty phase space with no attractors, and thus a zero velocity vector field. Upon receiving the random stimulus, the vector field deforms and eventually becomes smooth and deterministic, despite the random nature of the applied force, while the phase space develops various geometrical objects. We consider the simplest of these - gradient self-shaping systems, whose vector field is the gradient of some energy function, which under certain conditions develops into the multi-dimensional probability density distribution of the input. We explain how self-shaping systems are relevant to artificial neural networks. Firstly, we show that they can potentially perform pattern recognition tasks typically implemented by Hopfield neural networks, but without any supervision and on-line, and without developing spurious minima in the phase space. Secondly, they can reconstruct the probability density distribution of input signals, like probabilistic neural networks, but without the need for new training patterns to have to enter the network as new hardware units. We therefore regard self-shaping systems as a generalisation of the neural network concept, achieved by abandoning the "rigid units - flexible couplings'' paradigm and making the vector field fully flexible and amenable to external force. It is not clear how such systems could be implemented in hardware, and so this new concept presents an engineering challenge. It could also become an alternative paradigm for the modelling of both living and learning systems. Mathematically it is interesting to find how a self shaping system could develop non-trivial objects in the phase space such as periodic orbits or chaotic attractors. We investigate how a delayed vector field could form such objects. We show that this method produces chaos in a class systems which have very simple dynamics in the non-delayed case. We also demonstrate the coexistence of bounded and unbounded solutions dependent on the initial conditions and the value of the delay. Finally, we speculate about how such a method could be used in global optimization.
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SANSONE, ALESSANDRO. "Applications of Nonlinear Dynamics and Complex Systems Theory to Finance." Doctoral thesis, La Sapienza, 2007. http://hdl.handle.net/11573/917404.
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Sardanyés, i. Cayuela Josep. "Dynamics, evolution and information in nonlinear dynamical systems of replicators." Doctoral thesis, Universitat Pompeu Fabra, 2009. http://hdl.handle.net/10803/7182.
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En aquesta tesi he investigat diversos camps de la biologia que podrien englobar-se en la disciplina general dels sistemes no lineals de replicadors. Els treballs presentats en aquesta tesis investiguen diversos fenomens dinàmics i processos evolutius per virus de RNA, pels anomenats hipercicles i per models generals de replicadors antagonistes. Específicament he investigat les anomenades quasiespècies, utilitzades per a modelitzar poblacions de RNA. Els treballs sobre hipercicles exploren diversos fenomens previs a l'origen de la vida i a l'aparició de la primera cèl.lula vivent. Mitjançant models ecològics com també utilitzant diferents eines computacionals he estudiat l'anomenada hipòtesi de la Reina Roja per entitats replicadores simples amb mutació. Aquests estudis tenen un interès en el contexte de l'evolució prebiòtica i l'ecologia teòrica.In this thesis I have investigated several fields of biology that can be classified in the general subject of replicator nonlinear systems. The works presented in the thesis investigate several dynamical phenomena and evolutionary processes for RNA viruses, for hypercycles and for general models on antagonistic replicator dynamics. I have specifically investigated the dynamics of so-called quasispecies, used for the modelization of RNA populations. The works on hypercycles explore several phenomena related to previous events to the origin of life and to the appearance of the first living cell. By means of some ecologically-based mathematical models as well as of some computational models we also investigate the so-called Red Queen hypothesis for small, replicating-mutating entities. These studies are of interest in the context of prebiotic evolution and theoretical ecology.
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Sardanyés, Cayuela Josep. "Dynamics, evolution and information in nonlinear dynamical systems of replicators." Doctoral thesis, Universitat Pompeu Fabra, 2009. http://hdl.handle.net/10803/7182.
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En aquesta tesi he investigat diversos camps de la biologia que podrien englobar-se en la disciplina general dels sistemes no lineals de replicadors. Els treballs presentats en aquesta tesis investiguen diversos fenomens dinàmics i processos evolutius per virus de RNA, pels anomenats hipercicles i per models generals de replicadors antagonistes. Específicament he investigat les anomenades quasiespècies, utilitzades per a modelitzar poblacions de RNA. Els treballs sobre hipercicles exploren diversos fenomens previs a l'origen de la vida i a l'aparició de la primera cèl.lula vivent. Mitjançant models ecològics com també utilitzant diferents eines computacionals he estudiat l'anomenada hipòtesi de la Reina Roja per entitats replicadores simples amb mutació. Aquests estudis tenen un interès en el contexte de l'evolució prebiòtica i l'ecologia teòrica.In this thesis I have investigated several fields of biology that can be classified in the general subject of replicator nonlinear systems. The works presented in the thesis investigate several dynamical phenomena and evolutionary processes for RNA viruses, for hypercycles and for general models on antagonistic replicator dynamics. I have specifically investigated the dynamics of so-called quasispecies, used for the modelization of RNA populations. The works on hypercycles explore several phenomena related to previous events to the origin of life and to the appearance of the first living cell. By means of some ecologically-based mathematical models as well as of some computational models we also investigate the so-called Red Queen hypothesis for small, replicating-mutating entities. These studies are of interest in the context of prebiotic evolution and theoretical ecology.
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Bódai, Tamás. "Nonlinear ray dynamics in underwater acoustics." Available from the University of Aberdeen Library and Historic Collections Digital Resources, 2008. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=25875.
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González, Gómez Andrés. "Nonlinear dynamics and smooth transition models." Doctoral thesis, Handelshögskolan i Stockholm, Ekonomisk Statistik (ES), 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:hhs:diva-541.
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During the last few years nonlinear models have been a very active area of econometric research: new models have been introduced and existing ones generalized. To a large extent, these developments have concerned models in which the conditional moments are regime-dependent. In such models, the different regimes are usually linear and the change between them is governed by an observable or unobservable variable. These specifications can be useful in situations in which it is suspected that the behaviour of the dependent variable may vary between regimes. A classical example can be found the business cycle literature where it is argued that contractions in the economy are not only more violent but also short-lived than expansions. Unemployment, which tends to rise faster during recessions than decline during booms, constitutes another example. Two of the most popular regime-dependent models are the smooth transition and the threshold model. In both models cases the transition variable is observable but the specification of the way in which the model changes from one regime to the other is different. Particularly, in the smooth transition model the change is a continuous whereas in the threshold model it is abrupt. One of the factors that has influenced the development of nonlinear models are improvements in computer technology. They have not only permitted an introduction of more complex models but have also allowed the use of computer-intensive methods in hypothesis testing. This is particularly important in nonlinear models because there these methods have proved to be practical in testing statistical hypothesis such as linearity and parameter constancy. In general, these testing situation are not trivial and their solution often requires computer-intensive methods. In particular, bootstrapping and Monte Carlo testing are now commonly used. In this thesis the smooth transition model is used in different ways. In the first chapter, a vector smooth transition model is used as a device for deriving a test for parameter constancy in stationary vector autoregressive models. In the second chapter we introduce a panel model whose parameters can change in a smooth fashion between regimes as a function of an exogenous variable. The method is used to investigate whether financial constraints affect firms' \ investment decisions. The third chapter is concern with linearity testing in smooth transition models. New tests are introduced and Monte Carlo testing techniques are shown to be useful in achieving control over the size of the test. Finally, the last chapter is devoted to the Smooth Permanent Surge model. This is a nonlinear moving average model in which a shock can have transitory or permanent effects depending on its sign and magnitude. Test for linearity and random walk hypothesis are introduced.Diss. Stockholm : Handelshögsk., 2004
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Behdinan, Kamran. "Dynamics of geometrically nonlinear sliding beams." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ32734.pdf.
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Kim, Sangil. "Ensemble Filtering Methods for Nonlinear Dynamics." Diss., Tucson, Arizona : University of Arizona, 2005. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu%5Fetd%5F1101%5F1%5Fm.pdf&type=application/pdf.
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Wijewardane, Harshani Ovamini. "Nonlinear intersubband dynamics in semiconductor nanostructures." Diss., Columbia, Mo. : University of Missouri-Columbia, 2007. http://hdl.handle.net/10355/4744.
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Thesis (Ph. D.)--University of Missouri-Columbia, 2007.The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on December 17, 2007) Vita. Includes bibliographical references.
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al, Azad Abul Kalam. "Nonlinear synchrony dynamics of neuronal bursters." Thesis, University of Exeter, 2009. http://hdl.handle.net/10036/96226.
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We study the appearance of a novel phenomenon for coupled identical bursters: synchronized bursts where there are changes of spike synchrony within each burst. The examples we study are for normal form elliptic bursters where there is a periodic slow passage through a Bautin (codimension two degenerate Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf bifurcation at the onset of repetitive spiking while the end of burst occurs via a fold limit cycle bifurcation. We study synchronization behavior of two Bautin-type elliptic bursters for a linear direct coupling scheme as well as demonstrating its presence in an approximation of gap-junction and synaptic coupling. We also find similar behaviour in system consisted of three and four Bautin-type elliptic bursters. We note that higher order terms in the normal form that do not affect the behavior of a single burster can be responsible for changes in synchrony pattern; more precisely, we find within-burst synchrony changes associated with a turning point in the spontaneous spiking frequency (frequency transition). We also find multiple synchrony changes in similar system by incorporating multiple frequency transitions. To explain the phenomenon we considered a burst-synchronized constrained model and a bifurcation analysis of the this reduced model shows the existence of the observed within-burst synchrony states. Within-burst synchrony change is also found in the system of mutually delaycoupled two Bautin-type elliptic bursters with a constant delay. The similar phenomenon is shown to exist in the mutually-coupled conductance-based Morris-Lecar neuronal system with an additional slow variable generating elliptic bursting. We also find within-burst synchrony change in linearly coupled FitzHugh-Rinzel 2 3 elliptic bursting system where the synchrony change occurs via a period doubling bifurcation. A bifurcation analysis of a burst-synchronized constrained system identifies the periodic doubling bifurcation in this case. We show emergence of spontaneous burst synchrony cluster in the system of three Hindmarsh-Rose square-wave bursters with nonlinear coupling. The system is found to change between the available cluster states depending on the stimulus. Lyapunov exponents of the burst synchrony states are computed from the corresponding variational system to probe the stability of the states. Numerical simulation also shows existence of burst synchrony cluster in the larger network of such system.
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Bódai, Tamás. "Nonlinear ray dynamics in underwater acoustics." Thesis, University of Aberdeen, 2008. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=25875.
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This thesis is concerned with long-range sound propagation in deep water. The main area of interest is the stability of acoustic ray paths in wave guides in which there is a transition from single to double duct sound speed profiles, or vice-versa. Sound propagation is modelled within a ray theoretical framework, which facilitates a dynamical systems approach of understanding long-range propagation phenomena, and the use of its tools of analysis. Alternative reduction techniques to the Poincaré sections are presented, by which the stability of acoustic rays can be graphically determined. Beyond periodic driving, these techniques prove to be useful in case of the simplest quasiperiodic driving of the ray equations. One of the techniques facilitates a special representation of ray trajectories for periodic driving. Namely, the space of sectioned trajectories is partitioned into nonintersecting regular and chaotic regions as with the Poincaré sections, when quasiperiodic and chaotic trajectories are represented by curve segments and area filling points, respectively. In case of the simplest quasiperiodic driving – speaking about the same technique – regular trajectories are represented by curves similar to Lissajous curves, which are opened or closed depending on whether the two driving frequencies involved make relative primes or not. It is confirmed for a perturbed canonical profile that the background sound speed structure controls ray stability. It is also demonstrated for a particular double duct profile, when the singularity of the nonlinearity parameter for the homoclinic trajectory associated with this profile refers to the strong instability of corresponding perturbed trajectories.
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Sarnari, Francesco. "Nonlinear dynamics with broken reflection symmetry." Thesis, University of Leeds, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.487778.
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This research focuses on a one-dimensional reaction-diffusion dynamical system. Specifically, we examine the effects produced in a bounded domain by different sources of symmetry-breaking in the system. Such a source might be a throughflow, responsible for breaking the system's reflection symmetry.
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Jiad, Khalid Mohammed. "Nonlinear dynamics of optically pumped laser." Thesis, Heriot-Watt University, 1993. http://hdl.handle.net/10399/1403.
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Sutcliffe, Paul Michael. "Soliton dynamics in nonlinear planar systems." Thesis, Durham University, 1992. http://etheses.dur.ac.uk/10492/.
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The work in this thesis is concerned with the study of stability and scattering of solitons in planar models ie where spacetime is (2+l)-dimensional. We consider both integrable models, where exact solutions can be written in closed form, and non-integrable models, where approximations and numerical methods must be employed. In chapter III we use a 'collective coordinate' approximation to study the scattering of solitons in a model motivated by elementary particle physics. In chapter IV we discuss a method to obtain approximate soliton configurations which can then be used to investigate soliton dynamics. In chapter V we perform a test of the 'collective coordinate' approximation by applying it to the study of classical and quantum soliton scattering in an integrable model, where exact results are known. Chapters VI and VII are concerned with an integrable chiral model. First we construct exact solutions using twistor methods and then we go on to study soliton stability using numerical techniques. Through computer simulations we find that there exist solitons which scatter in a way unlike any previously found in integrable models. Furthermore, this soliton scattering resembles very closely that found in certain non-integrable models, thereby providing a link between the two classes. Finally, chapter VIII is an outlook on current and future research.
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Allen, Thomas. "The nonlinear dynamics of Langmuir circulations." Thesis, University of East Anglia, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293227.
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Halse, C. K. "Nonlinear dynamics of the automotive driveline." Thesis, University of Bristol, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.430171.
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Lim, Yan Hong. "Nonlinear dynamics of spacecraft power systems." Thesis, University of Surrey, 2000. http://epubs.surrey.ac.uk/2757/.
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This thesis pioneers the application of nonlinear dynamics to spacecraft power systems. Two areas of general interest are addressed. On the one hand, the fundamental dynamics of space power systems were investigated from a nonlineax dynamics perspective, and on the other, nonlinear dynamics concepts were used to realise a practical engineering application. The former examines four simple but relevant space power system models. The study revealed a variety of bifurcations, coexisting attractors and chaotic behaviour that could potentially shed light on some familiar but poorly understood effects in space power systems operations, including bus voltage collapse, spurious oscillations, and chaotic 'noise'. Because such behaviour manifests itself in nonlinear systems but could not be exposed by customary linear systems theory, potential anomalies may remain unpredicted which could lead to catastrophic consequences. As such, these results have important implications to reliability issues, critical in space. The exposition of the concepts and tools used in this thesis would serve the practising engineer by providing the basis and pave the way for studying larger and more complex systems, in the quest for improved system performance and reliability. In the course of this work, an algorithm to compute the maximum Lyapunov exponent from differential equations with discontinuities was required to confirm chaos. Although the concepts and tools for investigating smooth equations are well established, dynamics of non-smooth systems have not been extensively studied. Here, the algorithm proposed by Miiller to cope with the discontinuities in mechanics was reviewed and was found to be applicable to power electronics in general. As a confirmation, this algorithm was applied successfully to a well known Buck DC-DC converter. Although the exploitation of nonlinear dynamics to engineer direct practical applications is still in its infancy, one is presented in this thesis. A maximum power point tracker was synthesised via nonlinear dynamics principles, simulated and experimentally verified. Excellent static and dynamic performance were exhibited. In addition, a two-dimensional stroboscopic map was derived which adequately described the fundamental dynamics of the system. This is confirmed from the good agreement between the simulated and experimental return maps. Via this map and further bifurcation study, preliminary design guidelines were established.
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Voorsluijs, Valérie. "Emergent properties of nonlinear compartmentalised dynamics." Doctoral thesis, Universite Libre de Bruxelles, 2018. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/273993.
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Systems chemistry aims at studying and developing "smart" materials displaying reactivity to external stimuli, metabolism, self-repair abilities and self-replication properties. These features constitute the principal characteristics of living systems that smart materials tend to mimic. The synthesis strategies of these materials are still in their infancy, and identifying the mechanisms underlying emergent phenomena could lead to a better control and use of these behaviours in the synthesis of new materials. The complex dynamics of biological systems usually arises from the coupling of compartmentalised units in which nonlinear chemical reactions take place. In this thesis, we are interested in the complex dynamics emerging from such compartmentalisation of a reactive system. First, we analyse the impact of fluctuations of concentration on the dynamics of a chemical oscillatory reaction, namely the Belousov-Zhabotinsky reaction. We show that oscillations are more robust against fluctuations than other behaviours generated by the reaction (birhythmicity, chaos, ) and highlight different mechanisms by which oscillations can arise from fluctuations. Then, we study a model for chemical chaos, the so-called Willamowsky-Rössler model, in which we incorporate fluctuations and crowding effects. Fluctuations have a destructive effect on chaotic dynamics but when the reaction takes place on a surface where the different species can diffuse and react, a synergy develops between fluctuations, crowding effects and the mobility of the particles. This synergy enhances the re-emergence of chaos and the development of new behaviours. Finally, we show throughout different modelling approaches that compartmentalisation effects play a central role in the intracellular calcium dynamics and emphasise how microscopic properties of the system shape the global behaviour of this system. Compartmentalised nonlinear dynamics thus offer a wide range of future prospects for the synthesis of smart materials and fosters the development of nanoreactors based on these properties.Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Jafri, Firoz Ali Sajeed Ali. "Nonlinear Dynamics of Controlled Slipping Clutches." University of Cincinnati / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1179489414.
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Huang, Shu. "Investigating multiphoton phenomena using nonlinear dynamics." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/22558.
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Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2008.Committee Chair: Uzer, Turgay; Committee Member: Aral, Mustafa; Committee Member: Flannery, Raymond; Committee Member: Raman, Chandra; Committee Member: Schatz, Michael.
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Modi, Chetan O. "Nonlinear dynamics of a magnetoelastic system /." Online version of thesis, 1992. http://hdl.handle.net/1850/10849.
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Petviachvili, Nikolai. "Coherent structures in nonlinear plasma dynamics /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.
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Spencer, P. S. "Dynamics of semiconductor nonlinear optical waveguides." Thesis, University of Bath, 1993. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357408.
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ROTTNER, Matthias Christian. "Essays in macroeconomics and nonlinear dynamics." Doctoral thesis, European University Institute, 2021. https://hdl.handle.net/1814/71501.
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Defence date: 21 May 2021Examining Board: Professor Evi Pappa (Universidad Carlos III Madrid); Professor Leonardo Melosi (European University Institute and Federal Reserve Bank of Chicago); Professor Galo Nuño (Bank of Spain); Professor Andrea Prestipino (Federal Reserve Board)
This thesis investigates topics in macroeconomics with nonlinear dynamics as their inherent feature. It aims to further the understanding of the connection between the financial sector and economic fluctuations, challenges of monetary policy in a low interest rate environment and how to mitigate the macroeconomic consequences of a pandemic. The first chapter investigates the connection between the shadow banking sector and the vulnerability of the economy to a financial crisis. Motivated by the build-up of shadow bank leverage prior to the Great Recession, I develop a nonlinear macroeconomic model that features excessive leverage accumulation and show how this can cause a run. Introducing risk-shifting incentives to account for fluctuations in shadow bank leverage, I use the model to illustrate that extensive leverage makes the shadow banking system runnable, thereby raising the vulnerability of the economy to future financial crises. The model is taken to U.S. data with the objective of estimating the probability of a run in the years preceding the financial crisis of 2007-2008. The second chapter, joint with Francesco Bianchi and Leonardo Melosi, is motivated by the observation that the Federal Reserve Bank has been systematically undershooting its 2% inflation target in the past twenty years. This deflationary bias is a predictable consequence of the current symmetric monetary policy strategy that fails to recognize the risk of encountering the zero-lower-bound. An asymmetric rule according to which the central bank responds less aggressively to above-target inflation corrects the bias, improves welfare, and reduces the risk of deflationary spirals. The third chapter, joint with Matthieu Darracq Paries and Christoffer Kok, analyses the risk that an intended monetary policy accommodation might actually have contractionary effects in a low interest rate environment. We demonstrate that the risk of hitting the rate at which the effect reverses depends on the capitalization of the banking sector by using a nonlinear macroeconomic model. The framework suggests that the reversal interest rate is around −1% p.a. in the Euro Area. We show that the possibility of the reversal interest rate creates a novel motive for macroprudential policy. The fourth chapter, joint with Leonardo Melosi, studies contact tracing in a new macro-epidemiological model with asymptomatic spreaders. Contact tracing is a testing strategy that aims to reconstruct the infection chain of newly symptomatic agents. We show that contact tracing may be insufficient to stem the spread of infections because agents fail to internalize that their decisions increase the number of traceable contacts to be tested in the future. We provide theoretical underpinnings to the risk of becoming infected in macro-epidemiological models.
-- Part 1 Financial Crises and Shadow Banks: A Quantitative Analysis -- 1.1 Introduction -- 1.2 Model -- 1.3 Multiple Equilibria, Bank Runs and Leverage -- 1.4 Model Evaluation -- 1.5 Quantitative Assessment: Financial Crisis of 2007 - 2009 -- 1.6 Leverage Tax -- 1.7 Reduced Form Evidence: Quantile Regressions -- 1.8 Conclusion -- Part 2 Hitting the Elusive Inflation Target -- 2.1 Introduction -- 2.2 The Model -- 2.3 Deflationary Bias and Deflationary Spirals -- 2.4 ZLB Risk and Macroeconomic Biases -- 2.5 The Asymmetric Rule -- 2.6 Target Ranges -- 2.7 Conclusions -- Part 3 Reversal Interest Rate and Macroprudential Policy -- 3.1 Introduction -- 3.2 The Model -- 3.3 Calibration -- 3.4 Non-Linear Transmission, Reversal Interest Rate and Optimal Lower Bound -- 3.5 Macroprudential Policy -- 3.6 Conclusion -- Part 4 Pandemic Recessions and Contact Tracing -- 4.1 Introduction -- 4.2 The Model -- 4.3 Contact Tracing and Testing -- 4.4 Model Solution and Calibration -- 4.5 Quantitative Analysis of Contact Tracing -- 4.6 Extensions -- 4.7 Concluding Remarks -- References -- A Appendix to Chapter 1 -- B Appendix to Chapter 2 -- C Appendix to Chapter 3 -- D Appendix to Chapter 4
Chapter 1 ‘Financial Crises and Shadow Banks: A Quantitative Analysis' of the PhD thesis draws upon an earlier version published as EUI ECO 2021/02
Chapter 2 ‘Hitting the Elusive Inflation Target' of the PhD thesis draws upon an earlier version published as NBER Working Paper series, 2019/26279
Chapter 3 ‘Reversal Interest Rate and Macroprudential Policy' of the PhD thesis draws upon an earlier version published as ECB Working Paper;, 2020/2487.
Chapter 4 'Pandemic Recessions and Contact Tracing' of the PhD thesis draws upon an earlier version published as CEPR Discussion Paper, 2020/DP15482.
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Hughes, Jonathan L. "Applications of Stability Analysis to Nonlinear Discrete Dynamical Systems Modeling Interactions." VCU Scholars Compass, 2015. http://scholarscompass.vcu.edu/etd/3819.
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Many of the phenomena studied in the natural and social sciences are governed by processes which are discrete and nonlinear in nature, while the most highly developed and commonly used mathematical models are linear and continuous. There are significant differences between the discrete and the continuous, the nonlinear and the linear cases, and the development of mathematical models which exhibit the discrete, nonlinear properties occurring in nature and society is critical to future scientific progress. This thesis presents the basic theory of discrete dynamical systems and stability analysis and explores several applications of this theory to nonlinear systems which model interactions involving economic agents and biological populations. In particular we will explore the stability properties of equilibria associated with inter-species and intergenerational population dynamics in biology and market price and agent composition dynamics in economics.
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Homer, Martin Edward. "Bifurcations and dynamics of piecewise smooth dynamical systems of arbitrary dimension." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299271.
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Beaver, Stefanie Rene'. "Input-ouput approximation for nonlinear structural dynamics." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1398.
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Morales, Molina Luis Yansi. "Ratchet dynamics in nonlinear Klein-Gordon systems." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=974449865.
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Walter, Kevin Robert. "The nonlinear dynamics of the sea breeze." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1265.
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The response of the land and sea breeze circulation to two highly simplified dynamical models is presented. The first dynamical model is the explicit specification of an oscillating interior heat source analogous to that from Rotunno (1983). Emphasis is placed on the variation of the response with heating amplitude and latitude. In addition, a weakly nonlinear analysis focuses on the dynamic forcing of nonlinear features such as a semi-diurnal gravity wave, fronts, and asymmetry in the magnitude of onshore and offshore flow. One surprising result is the identification of a cycle-mean surface divergence pattern at both 0? and 45?. At 45?, this divergence pattern is accompanied by a cycle mean shore-parallel response due to the Earth's rotation.
The second dynamical model is the explicit specification of an oscillating surface heat flux. Again, comparison is made between simulations at different heating amplitudes, and between simulations at different latitudes. To address changes in the solution due to the heating method itself, comparison is made between solutions from the surface heating method and solutions from the interior heating method. Finally, solutions across the planetary continuum are explored for critical latitude dependence in high-amplitude simulations.