Relevant bibliographies by topics / Non-autonomous dynamical systems

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Non-autonomous dynamical systems'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Non-autonomous dynamical systems"

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N. Carvalho, Alexandre, José A. Langa, and James C. Robinson. "Non-autonomous dynamical systems." Discrete & Continuous Dynamical Systems - B 20, no. 3 (2015): 703–47. http://dx.doi.org/10.3934/dcdsb.2015.20.703.

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Anzaldo-Meneses, A. "On non-autonomous dynamical systems." Journal of Mathematical Physics 56, no. 4 (April 2015): 042702. http://dx.doi.org/10.1063/1.4916893.

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Cavro, Jakub. "Recurrence in non-autonomous dynamical systems." Journal of Difference Equations and Applications 25, no. 9-10 (August 9, 2019): 1404–11. http://dx.doi.org/10.1080/10236198.2019.1651849.

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Momeni, Davood, Phongpichit Channuie, and Mudhahir Al Ajmi. "Mapping of non-autonomous dynamical systems to autonomous ones." International Journal of Geometric Methods in Modern Physics 16, no. 06 (June 2019): 1950089. http://dx.doi.org/10.1142/s0219887819500890.

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Using a proper choice of the dynamical variables, we show that a non-autonomous dynamical system transforming to an autonomous dynamical system with a certain coordinate transformations can be obtained by solving a general nonlinear first-order partial differential equations. We examine some special cases and provide particular physical examples. Our framework constitutes general machineries in investigating other non-autonomous dynamical systems.
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Cheban, David. "Sell’s conjecture for non-autonomous dynamical systems." Nonlinear Analysis: Theory, Methods & Applications 75, no. 7 (May 2012): 3393–406. http://dx.doi.org/10.1016/j.na.2012.01.002.

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Leon, Manuel de, and Paulo R. Rodrigues. "Dynamical connections and non-autonomous lagrangian systems." Annales de la faculté des sciences de Toulouse Mathématiques 9, no. 2 (1988): 171–81. http://dx.doi.org/10.5802/afst.655.

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Huang, Qiuling, Yuming Shi, and Lijuan Zhang. "Sensitivity of non-autonomous discrete dynamical systems." Applied Mathematics Letters 39 (January 2015): 31–34. http://dx.doi.org/10.1016/j.aml.2014.08.007.

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Schechter, Martin. "Periodic non-autonomous second-order dynamical systems." Journal of Differential Equations 223, no. 2 (April 2006): 290–302. http://dx.doi.org/10.1016/j.jde.2005.02.022.

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Shao, Hua, Hao Zhu, and Guanrong Chen. "On fuzzifications of non-autonomous dynamical systems." Topology and its Applications 297 (June 2021): 107704. http://dx.doi.org/10.1016/j.topol.2021.107704.

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Chen, Xiaopeng, and Jinqiao Duan. "State space decomposition for non-autonomous dynamical systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 5 (September 26, 2011): 957–74. http://dx.doi.org/10.1017/s0308210510000661.

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The decomposition of state spaces into dynamically different components is helpful for understanding dynamics of complex systems. A Conley-type decomposition theorem is proved for non-autonomous dynamical systems defined on a non-compact but separable state space. Specifically, the state space can be decomposed into a chain-recurrent part and a gradient-like part. This result applies to both non-autonomous ordinary differential equations on a Euclidean space (which is only locally compact), and to non-autonomous partial differential equations on an infinite-dimensional function space (which is not even locally compact). This decomposition result is demonstrated by discussing a few concrete examples, such as the Lorenz system and the Navier–Stokes system, under time-dependent forcing.
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Dissertations / Theses on the topic "Non-autonomous dynamical systems"

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Atnip, Jason. "Conformal and Stochastic Non-Autonomous Dynamical Systems." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1248519/.

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In this dissertation we focus on the application of thermodynamic formalism to non-autonomous and random dynamical systems. Specifically we use the thermodynamic formalism to investigate the dimension of various fractal constructions via the, now standard, technique of Bowen which he developed in his 1979 paper on quasi-Fuchsian groups. Bowen showed, roughly speaking, that the dimension of a fractal is equal to the zero of the relevant topological pressure function. We generalize the results of Rempe-Gillen and Urbanski on non-autonomous iterated function systems to the setting of non-autonomous graph directed Markov systems and then show that the Hausdorff dimension of the fractal limit set is equal to the zero of the associated pressure function provided the size of the alphabets at each time step do not grow too quickly. In trying to remove these growth restrictions, we present several other systems for which Bowen's formula holds, most notably ascending systems. We then use these various constructions to investigate the Hausdorff dimension of various subsets of the Julia set for different large classes of transcendental meromorphic functions of finite order which have been perturbed non-autonomously. In particular we find lower and upper bounds for the dimension of the subset of the Julia set whose points escape to infinity, and in many cases we find the exact dimension. While the upper bound was known previously in the autonomous case, the lower bound was not known in this setting, and all of these results are new in the non-autonomous setting. We also use transfer operator techniques to prove an almost sure invariance principle for random dynamical systems for which the thermodynamical formalism has been well established. In particular, we see that if a system exhibits a fiberwise spectral gap property and the base dynamical system is sufficiently well behaved, i.e. it exhibits an exponential decay of correlations, then the almost sure invariance principle holds. We then apply these results to uniformly expanding random systems like those studied by Mayer, Skorulski, and Urbanski and Denker and Gordin.
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Stonier, D. J., and mikewood@deakin edu au. "Stability theory and numerical analysis of non-autonomous dynamical systems." Deakin University. School of Information Technology, 2003. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051125.113243.

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The development and use of cocycles for analysis of non-autonomous behaviour is a technique that has been known for several years. Initially developed as an extension to semi-group theory for studying rion-autonornous behaviour, it was extensively used in analysing random dynamical systems [2, 9, 10, 12]. Many of the results regarding asymptotic behaviour developed for random dynamical systems, including the concept of cocycle attractors were successfully transferred and reinterpreted for deterministic non-autonomous systems primarily by P. Kloeden and B. Schmalfuss [20, 21, 28, 29]. The theory concerning cocycle attractors was later developed in various contexts specific to particular classes of dynamical systems [6, 7, 13], although a comprehensive understanding of cocycle attractors (redefined as pullback attractors within this thesis) and their role in the stability of non-autonomous dynamical systems was still at this stage incomplete. It was this purpose that motivated Chapters 1-3 to define and formalise the concept of stability within non-autonomous dynamical systems. The approach taken incorporates the elements of classical asymptotic theory, and refines the notion of pullback attraction with further development towards a study of pull-back stability arid pullback asymptotic stability. In a comprehensive manner, it clearly establishes both pullback and forward (classical) stability theory as fundamentally unique and essential components of non-autonomous stability. Many of the introductory theorems and examples highlight the key properties arid differences between pullback and forward stability. The theory also cohesively retains all the properties of classical asymptotic stability theory in an autonomous environment. These chapters are intended as a fundamental framework from which further research in the various fields of non-autonomous dynamical systems may be extended. A preliminary version of a Lyapunov-like theory that characterises pullback attraction is created as a tool for examining non-autonomous behaviour in Chapter 5. The nature of its usefulness however is at this stage restricted to the converse theorem of asymptotic stability. Chapter 7 introduces the theory of Loci Dynamics. A transformation is made to an alternative dynamical system where forward asymptotic (classical asymptotic) behaviour characterises pullback attraction to a particular point in the original dynamical system. This has the advantage in that certain conventional techniques for a forward analysis may be applied. The remainder of the thesis, Chapters 4, 6 and Section 7.3, investigates the effects of perturbations and discretisations on non-autonomous dynamical systems known to possess structures that exhibit some form of stability or attraction. Chapter 4 investigates autonomous systems with semi-group attractors, that have been non-autonomously perturbed, whilst Chapter 6 observes the effects of discretisation on non-autonomous dynamical systems that exhibit properties of forward asymptotic stability. Chapter 7 explores the same problem of discretisation, but for pullback asymptotically stable systems. The theory of Loci Dynamics is used to analyse the nature of the discretisation, but establishment of results directly analogous to those discovered in Chapter 6 is shown to be unachievable. Instead a case by case analysis is provided for specific classes of dynamical systems, for which the results generate a numerical approximation of the pullback attraction in the original continuous dynamical system. The nature of the results regarding discretisation provide a non-autonomous extension to the work initiated by A. Stuart and J. Humphries [34, 35] for the numerical approximation of semi-group attractors within autonomous systems. . Of particular importance is the effect on the system's asymptotic behaviour over non-finite intervals of discretisation.
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Lopez, Marco Antonio. "Hausdorff Dimension of Shrinking-Target Sets Under Non-Autonomous Systems." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1248505/.

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For a dynamical system on a metric space a shrinking-target set consists of those points whose orbit hit a given ball of shrinking radius infinitely often. Historically such sets originate in Diophantine approximation, in which case they describe the set of well-approximable numbers. One aspect of such sets that is often studied is their Hausdorff dimension. We will show that an analogue of Bowen's dimension formula holds for such sets when they are generated by conformal non-autonomous iterated function systems satisfying some natural assumptions.
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Horenkamp, Christian [Verfasser]. "Efficient detection of coherent structures in non-autonomous dynamical systems via transfer operator methods / Christian Horenkamp." Paderborn : Universitätsbibliothek, 2014. http://d-nb.info/1052264263/34.

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Prieto, Martínez Pere Daniel. "Geometrical structures of higher-order dynamical systems and field theories." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/284215.

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Geometrical physics is a relatively young branch of applied mathematics that was initiated by the 60's and the 70's when A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, among many others, began to study various topics in physics using methods of differential geometry. This "geometrization" provides a way to analyze the features of the physical systems from a global viewpoint, thus obtaining qualitative properties that help us in the integration of the equations that describe them. Since then, there has been a strong development in the intrinsic treatment of a variety of topics in theoretical physics, applied mathematics and control theory using methods of differential geometry. Most of the work done in geometrical physics since its first days has been devoted to study first-order theories, that is, those theories whose physical information depends on (at most) first-order derivatives of the generalized coordinates of position (velocities). However, there are theories in physics in which the physical information depends explicitly on accelerations or higher-order derivatives of the generalized coordinates of position, and thus more sophisticated geometrical tools are needed to model them acurately. In this Ph.D. Thesis we pretend to give a geometrical description of some of these higher-order theories. In particular, we focus on dynamical systems and field theories whose dynamical information can be given in terms of a Lagrangian function, or a Hamiltonian that admits Lagrangian counterpart. More precisely, we will use the Lagrangian-Hamiltonian unified approach in order to develop a geometric framework for autonomous and non-autonomous higher-order dynamical system, and for second-order field theories. This geometric framework will be used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.
La física geomètrica és una branca relativament jove de la matemàtica aplicada que es va iniciar als anys 60 i 70 qua A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, entre molts altres, van començar a estudiar diversos problemes en física usant mètodes de geometria diferencial. Aquesta "geometrització" proporciona una manera d'analitzar les característiques dels sistemes físics des d'una perspectiva global, obtenint així propietats qualitatives que faciliten la integració de les equacions que els descriuen. D'ençà s'ha produït un fort desenvolupamewnt en el tractament intrínsic d'una gran varietat de problemes en física teòrica, matemàtica aplicada i teoria de control usant mètodes de geometria diferencial. Gran part del treball realitzat en la física geomètrica des dels seus primers dies s'ha dedicat a l'estudi de teories de primer ordre, és a dir, teories tals que la informació física depèn en, com a molt, derivades de primer ordre de les coordenades de posició generalitzades (velocitats). Tanmateix, hi ha teories en física en les que la informació física depèn de manera explícita en acceleracions o derivades d'ordre superior de les coordenades de posició generalitzades, requerint, per tant, d'eines geomètriques més sofisticades per a modelar-les de manera acurada. En aquesta Tesi Doctoral ens proposem donar una descripció geomètrica d'algunes d'aquestes teories. En particular, estudiarem sistemes dinàmics i teories de camps tals que la seva informació dinàmica ve donada en termes d'una funció lagrangiana, o d'un hamiltonià que prové d'un sitema lagrangià. Per a ser més precisos emprarem la formulació unificada Lagrangiana-Hamiltoniana per tal de desenvolupar marcs geomètrics per a sistemes dinàmics d'ordre superior autònoms i no autònoms, i per a teories de camps de segon ordre. Amb aquest marc geomètric estudiarem alguns exemples físics rellevants i algunes aplicacions, com la teoria de Hamilton-Jacobi per a sistemes mecànics d'ordre superior, partícules relativístiques amb spin i problemes de deformació en mecànica, i l'equació de Korteweg-de Vries i altres sistemes en teories de camps.
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Kopylov, Nikita. "Magnus-based geometric integrators for dynamical systems with time-dependent potentials." Doctoral thesis, Universitat Politècnica de València, 2019. http://hdl.handle.net/10251/118798.

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[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la mecánica cuántica, clásica y celestial. La meta de la tesis es construir integradores para unos problemas relevantes no autónomos: la ecuación de Schrödinger, que es el fundamento de la mecánica cuántica; las ecuaciones de Hill y de onda, que describen sistemas oscilatorios; el problema de Kepler con la masa variante en el tiempo. El Capítulo 1 describe la motivación y los objetivos de la obra en el contexto histórico de la integración numérica. En el Capítulo 2 se introducen los conceptos esenciales y unas herramientas fundamentales utilizadas a lo largo de la tesis. El diseño de los integradores propuestos se basa en los métodos de composición y escisión y en el desarrollo de Magnus. En el Capítulo 3 se describe el primero. Su idea principal consta de una recombinación de unos integradores sencillos para obtener la solución del problema. El concepto importante de las condiciones de orden se describe en ese capítulo. En el Capítulo 4 se hace un resumen de las álgebras de Lie y del desarrollo de Magnus que son las herramientas algebraicas que permiten expresar la solución de ecuaciones diferenciales dependientes del tiempo. La ecuación lineal de Schrödinger con potencial dependiente del tiempo está examinada en el Capítulo 5. Dado su estructura particular, nuevos métodos casi sin conmutadores, basados en el desarrollo de Magnus, son construidos. Su eficiencia es demostrada en unos experimentos numéricos con el modelo de Walker-Preston de una molécula dentro de un campo electromagnético. En el Capítulo 6, se diseñan los métodos de Magnus-escisión para las ecuaciones de onda y de Hill. Su eficiencia está demostrada en los experimentos numéricos con varios sistemas oscilatorios: con la ecuación de Mathieu, la ec. de Hill matricial, las ecuaciones de onda y de Klein-Gordon-Fock. El Capítulo 7 explica cómo el enfoque algebraico y el desarrollo de Magnus pueden generalizarse a los problemas no lineales. El ejemplo utilizado es el problema de Kepler con masa decreciente. El Capítulo 8 concluye la tesis, reseña los resultados y traza las posibles direcciones de la investigación futura.
[CAT] Aquesta tesi tracta de la integració numèrica de sistemes hamiltonians amb potencials explícitament dependents del temps. Els problemes d'aquest tipus són comuns en la física matemàtica, perquè provenen de la mecànica quàntica, clàssica i celest. L'objectiu de la tesi és construir integradors per a uns problemes rellevants no autònoms: l'equació de Schrödinger, que és el fonament de la mecànica quàntica; les equacions de Hill i d'ona, que descriuen sistemes oscil·latoris; el problema de Kepler amb la massa variant en el temps. El Capítol 1 descriu la motivació i els objectius de l'obra en el context històric de la integració numèrica. En Capítol 2 s'introdueixen els conceptes essencials i unes ferramentes fonamentals utilitzades al llarg de la tesi. El disseny dels integradors proposats es basa en els mètodes de composició i escissió i en el desenvolupament de Magnus. En el Capítol 3, es descriu el primer. La seua idea principal consta d'una recombinació d'uns integradors senzills per a obtenir la solució del problema. El concepte important de les condicions d'orde es descriu en eixe capítol. El Capítol 4 fa un resum de les àlgebres de Lie i del desenvolupament de Magnus que són les ferramentes algebraiques que permeten expressar la solució d'equacions diferencials dependents del temps. L'equació lineal de Schrödinger amb potencial dependent del temps està examinada en el Capítol 5. Donat la seua estructura particular, nous mètodes quasi sense commutadors, basats en el desenvolupament de Magnus, són construïts. La seua eficiència és demostrada en uns experiments numèrics amb el model de Walker-Preston d'una molècula dins d'un camp electromagnètic. En el Capítol 6 es dissenyen els mètodes de Magnus-escissió per a les equacions d'onda i de Hill. El seu rendiment està demostrat en els experiments numèrics amb diversos sistemes oscil·latoris: amb l'equació de Mathieu, l'ec. de Hill matricial, les equacions d'onda i de Klein-Gordon-Fock. El Capítol 7 explica com l'enfocament algebraic i el desenvolupament de Magnus poden generalitzar-se als problemes no lineals. L'exemple utilitzat és el problema de Kepler amb massa decreixent. El Capítol 8 conclou la tesi, ressenya els resultats i traça les possibles direccions de la investigació futura.
[EN] The present thesis addresses the numerical integration of Hamiltonian systems with explicitly time-dependent potentials. These problems are common in mathematical physics because they come from quantum, classical and celestial mechanics. The goal of the thesis is to construct integrators for several import ant non-autonomous problems: the Schrödinger equation, which is the cornerstone of quantum mechanics; the Hill and the wave equations, that describe oscillating systems; the Kepler problem with time-variant mass. Chapter 1 describes the motivation and the aims of the work in the historical context of numerical integration. In Chapter 2 essential concepts and some fundamental tools used throughout the thesis are introduced. The design of the proposed integrators is based on the composition and splitting methods and the Magnus expansion. In Chapter 3, the former is described. Their main idea is to recombine some simpler integrators to obtain the solution. The salient concept of order conditions is described in that chapter. Chapter 4 summarises Lie algebras and the Magnus expansion ¿ algebraic tools that help to express the solution of time-dependent differential equations. The linear Schrödinger equation with time-dependent potential is considered in Chapter 5. Given its particular structure, new, Magnus-based quasi-commutator-free integrators are build. Their efficiency is shown in numerical experiments with the Walker-Preston model of a molecule in an electromagnetic field. In Chapter 6, Magnus-splitting methods for the wave and the Hill equations are designed. Their performance is demonstrated in numerical experiments with various oscillatory systems: the Mathieu equation, the matrix Hill eq., the wave and the Klein-Gordon-Fock eq. Chapter 7 shows how the algebraic approach and the Magnus expansion can be generalised to non-linear problems. The example used is the Kepler problem with decreasing mass. The thesis is concluded by Chapter 8, in which the results are reviewed and possible directions of future work are outlined.
Kopylov, N. (2019). Magnus-based geometric integrators for dynamical systems with time-dependent potentials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/118798
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Acevedo, Jeovanny de Jesus Muentes. "Famílias Anosov: estabilidade estrutural, variedades invariantes, e entropía para sistemas dinâmicos não-estacionários." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-06122017-113522/.

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As famílias Anosov foram introduzidas por P. Arnoux e A. Fisher, motivados por generalizar a noção de difeomorfismo de Anosov. A grosso modo, as famílias Anosov são sequências de difeomorfismos (fi)i∈Z definidos em uma sequencia de variedades Riemannianas compactas (Mi)i∈Z, em que fi: Mi ->Mi+1 para todo i ∈ Z, tal que a composição fi+no· · ·ofi, para n >=1, tem comportamento assintoticamente hiperbólico. Esta noção é conhecida como um sistema dinâmico não-estacionário ou um sistema dinâmico não-autônomo. Sejam M a união disjunta de cada Mi, para i ∈ Z, e Fm(M) o conjunto consistente das famílias de difeomorfismos (fi)i∈Z de classe Cm definidos na sequência (Mi)i∈Z. O propósito principal deste trabalho é mostrar algumas propriedades das famílias Anosov. Em particular, mostraremos que o conjunto destas famílias é aberto em Fm(M), em que Fm(M) é munido da topologia forte (ou topologia Whitney); a estabilidade estrutural de certa classe de famílias Anosov, considerando conjugações topológicas uniformes; e várias versões para os Teoremas de variedades estáveis e instáveis. Os resultados que serão apresentados aqui generalizam alguns outros resultados obtidos em Sistemas Dinâmicos Aleatórios, os quais serão mencionados ao longo do trabalho. Além do anterior, será introduzida a entropia topológica para elementos em Fm(M) e mostraremos algumas das suas propriedades. Provaremos que esta entropia é contínua em Fm(M) munido da topologia forte. Porém, ela é descontínua em cada elemento de Fm(M) munido da topologia produto. Também apresentaremos um resultado que pode ser uma ferramenta de muita utilidade no estudo da continuidade da entropia topológica de difeomorfismos definidos em variedades compactas. Finalizaremos o trabalho dando uma lista de problemas que surgiram ao longo desta pesquisa e que serão analisados em um trabalho futuro.
Anosov families were introduced by P. Arnoux and A. Fisher, motivated by generalizing the notion of Anosov dieomorphisms. Roughly, Anosov families are sequences of dieomorphisms (fi)i∈Z dened on a sequence of compact Riemannian manifolds (Mi)i∈Z, where fi: Mi -> Mi+1 for all i ∈ Z, such that the composition fi+n o · · · o fi, for n >=1, has asymptotically hyperbolic behavior. This notion is known as a non-stationary dynamical system or a non-autonomous dynamical system. Let M be the disjoint union of each Mi, for each i ∈ Z, and Fm(M) the set consisting of families of Cm-dieomorphisms (fi)i∈Z dened on the sequence (Mi)i∈Z. The main goal of this work is to explore some properties of Anosov families. In particular, we will show that the set consisting of these families is open in Fm(M), where Fm(M) is endowed with the strong topology (or Whitney topology); the structural stability of a certain class of Anosov families, considering uniform topological conjugacies; and some versions of stable and unstable manifold theorems. The results that will be presented here generalize some results obtained in Random Dynamical Systems, which will be mentioned throughout the work. In addition to the above mentioned theorems, the topological entropy for elements in Fm(M) will be introduced, and we will show some of its properties. We will prove that this entropy is continuous on Fm(M) endowed with strong topology. However, it is discontinuous at each element of Fm(M) endowed with the product topology. We will also present a result that can be a very useful tool in the study of the continuity of the topological entropy of dieomorphisms dened on compact manifolds. We will nish the work by giving a list of problems that have arisen throughout this research and that will be analyzed in a future work.
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Mostefaoui, Imene Meriem. "Analyse mathématique d’un système dynamique/réaction-diffusion modélisant la distribution des bactéries résistantes aux antibiotiques dans les rivières." Thesis, La Rochelle, 2014. http://www.theses.fr/2014LAROS020/document.

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L'objectif de cette thèse est l'étude qualitative de certains modèles de la dynamique et la distribution des bactéries dans une rivière. Il s'agit de la stabilité des états stationnaires et l'existence des solutions périodiques. Nous considérons, dans la première partie de la thèse, un système d'équations différentielles ordinaires qui modélise les interactions et la dynamique de quatre espèces de bactéries dans une rivière. Nous avons étudié le comportement asymptotique des états stationnaires. L'étude de la stabilité des états stationnaires est essentiellement faite par la construction d'une fonction de Lyapunov combinée avec le principe d'invariance de LaSalle. D'autre part, l'existence des solutions périodiques est démontrée en utilisant le théorème de continuation de Mawhin. La deuxième partie de la thèse est consacrée à l'étude d'un système de convection-diffusion non-autonome. Ce modèle tient compte du transport des bactéries. Nous étudions l'analyse qualitative des solutions, nous déterminons l'ensemble limite du système et nous démontrons l'existence des états stationnaires positifs. L'étude de l'existence des états stationnaires (les seuls qu'il soit possible d'obtenir) est basée sur le théorème de Leray-Schauder
The objective of this thesis is the qualitative study of some models of the dynamic and the distribution of bacteria in a river. We are interested in the stability of equilibria and the existence of periodic solutions. The thesis can be divided into two parts; the first part is concerned with a mathematical analysis of a system of differential equations modelling the dynamics and the interactions of four species of bacteria in a river. The asymptotic behavior of equilibria is established. The stability study of equilibrium states is mainly done by construction of Lyapunov functions combined with LaSalle's invariance principle. On the other hand, the existence of periodic solutions is proved under certain conditions using the continuation theorem of Mawhin. In the second part of this thesis, we propose a non-autonomous convection-reaction diffusion system with nonlinear reaction source functions. This model refers to the quantification and the distribution of antibiotic resistant bacteria (ARB) in a river. Our main contributions are : (i) the determination of the limit set of the system; it is shown that it is reduced to the solutions of the associated elliptic system; (ii) sufficient conditions for the existence of a positive solution of the associated elliptic system based on the Leray Schauder's degree theory
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Kirven, Thomas C. "AUTONOMOUS QUADROTOR COLLISION AVOIDANCE AND DESTINATION SEEKING IN A GPS-DENIED ENVIRONMENT." UKnowledge, 2017. https://uknowledge.uky.edu/me_etds/105.

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This thesis presents a real-time autonomous guidance and control method for a quadrotor in a GPS-denied environment. The quadrotor autonomously seeks a destination while it avoids obstacles whose shape and position are initially unknown. We implement the obstacle avoidance and destination seeking methods using off-the-shelf sensors, including a vision-sensing camera. The vision-sensing camera detects the positions of points on the surface of obstacles. We use this obstacle position data and a potential-field method to generate velocity commands. We present a backstepping controller that uses the velocity commands to generate the quadrotor's control inputs. In indoor experiments, we demonstrate that the guidance and control methods provide the quadrotor with sufficient autonomy to fly point to point, while avoiding obstacles.
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Kunz, Vandeni Clarice. "Modulação autonômica da frequência cardíaca e sua relação com os fatores de risco e o polimorfismo do gene da ECA de pacientes com doença arterial coronariana." Universidade Federal de São Carlos, 2012. https://repositorio.ufscar.br/handle/ufscar/5140.

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Universidade Federal de Sao Carlos
The multifactorial nature of coronary artery disease (CAD) includes complications related to angina and acute myocardial infarction (AMI) and disorders involving sympathetic and parasympathetic cardiac autonomic modulation. The objective of this study was to evaluate the autonomic modulation of heart rate (HR) by linear and non-linear methods in healthy men and in patients with AMI and different percentages of coronary stenosis, as well as its relation with CAD risk factors. In order to evaluate heart rate variability (HRV), the HR and the RR intervals were recorded for 15 min in the supine position. Based on the results of this study, three manuscripts were written: The first manuscript presents the results of 10 men with AMI (57±9 years old) (2nd and 7th day after coronary event) and 11 healthy men (53±4 years old). The HRV analysis was carried out using linear methods in the time domain (TD=RMSSD and SDNN) and frequency domain (FD= low frequency (LF) and high frequency (HF) in normalized units (nu) and LF/HF) and using the non-linear methods approximate entropy (ApEn). A significant relationship between the linear and non-linear methods and the RMSSD, SDNN, LFun, HFun and LF/HF and ApEn indexes was observed. The linear and non-linear HRV indexes from the healthy group were higher than those of the AMI group on the 2nd and 7th days, which suggests that the analysis of HRV with linear methods in the TD and FD and the use of ApEn for linear analysis are in agreement, both for healthy subjects and patients after AMI. The second manuscript presents the results of 52 men (54±5 years old) divided into two groups with coronary obstruction CAD+ ≥ 50% (n=18) and CAD- < 50% (n=17) and one control group (n=17). HRV analysis was carried out with Shannon entropy (SE) and symbolic analysis (0V and 2ULV). The patients with DAC+ presented lower SE (complexity), 2ULV (vagal predominance) and higher 0V (sympathetic predominance) than the DAC- and control groups, which indicates that cardiac autonomic disorder is related to the degree of coronary occlusion and to cardiac impairment. The third manuscript presents the results for risk factors, ACE I/D polymorphism and the indexes in the TD and FD of 151 patients with CAD (56±8 years old, DD=54, DI=70 and II=27). The results show that there was no relation between the ACE I/D polymorphism and HR, BP or HRV. However, the highest indexes of the HRV, which reflect vagal autonomic modulation, are related to a lower percentage of stenosis and the use of ACE inhibitors.
A doença arterial coronariana (DAC) é de natureza multifatorial sendo que as principais complicações estão relacionadas à angina e infarto agudo do miocárdio (IAM), apresentando disfunção da modulação autonômica cardíaca simpática e parassimpática. Assim, o objetivo foi avaliar a modulação autonômica da frequência cardíaca (FC), a partir de métodos lineares e não lineares, de homens saudáveis, de pacientes com IAM e com diferentes percentuais de estenose coronariana e sua relação com os fatores de risco para a DAC. Para a análise da variabilidade da FC (VFC) foi realizada a captação dos intervalos RR e da FC, durante 15 min na posição supina. A partir dos resultados do estudo foram elaborados três manuscritos. Primeiro manuscrito: Foram apresentados os resultados de 10 homens com IAM (57±9 anos) (avaliados no 2º e 7 º dia após evento coronariano) e 11 homens saudáveis (53±4 anos). A análise da VFC foi realizada utilizando-se dos métodos lineares no domínio do tempo (DT=RMSSD e RMSM) e da frequência (DF=baixa frequência (BF) e alta frequência (AF) em unidades normalizadas (un) e BF/AF) e pelo método não linear de entropia aproximada (EnAp). As análises da relação entre os métodos lineares e o não linear (índices RMSSD, RMSM, BFun, AFun e BF/AF com a EnAp) foi significativa. Os índices lineares e não linear da VFC do grupo saudável foram maiores em relação ao grupo IAM no 2º e no 7º dia. Os resultados mostram que os métodos lineares no DT e no DF e o não linear , são concordantes, para análise da VFC, tanto para voluntários saudáveis como para pacientes após o IAM. Segundo manuscrito: Foram apresentados os resultados de 52 homens (54±5 anos) divididos em três grupos, sendo dois grupos com obstrução coronariana DAC+ (≥ 50%; n=18) e DAC- (< 50%; n=17) e um grupo controle (n=17). A análise da VFC foi pela entropia de Shannon (ES) e análise simbólica (0V e 2ULV). Os pacientes com DAC+ apresentam menor ES (complexidade) e 2ULV (predominância vagal) e maior 0V (predominância simpática) quando comparado aos grupos DAC- e controle, o que indica que a disfunção autonômica cardíaca está relacionada ao grau de oclusão coronariana. Terceiro manuscrito: Foram apresentados os resultados da possível relação existente entre dos fatores de risco, do polimorfismo I/D do gene da ECA com os índices no DT e no DF de 151 pacientes com DAC (56±8 anos, DD=54, DI=70 e II=27). Os resultados mostram que não há relação entre o polimorfismo I/D do gene da ECA com a FC, PA e VFC. Já os maiores índices da VFC que refletem a modulação autonômica vagal estão relacionados ao menor percentual de estenose e ao uso de inibidores da ECA.
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Books on the topic "Non-autonomous dynamical systems"

1

Global attractors of non-autonomous dissipative dynamical systems. Singapore: World Scientific, 2005.

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Carvalho, Alexandre N. Attractors for infinite-dimensional non-autonomous dynamical systems. New York, NY: Springer New York, 2013.

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Carvalho, Alexandre N., José A. Langa, and James C. Robinson. Attractors for infinite-dimensional non-autonomous dynamical systems. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-4581-4.

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Capietto, Anna. Stability and Bifurcation Theory for Non-Autonomous Differential Equations: Cetraro, Italy 2011, Editors: Russell Johnson, Maria Patrizia Pera. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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Lyapunov Stability of Non-Autonomous Dynamical Systems. Nova Science Pub Inc, 2013.

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Robinson, James, Alexandre Carvalho, and José A. Langa. Attractors for infinite-dimensional non-autonomous dynamical systems. Springer, 2012.

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Robinson, James, Alexandre Carvalho, and José A. Langa. Attractors for infinite-dimensional non-autonomous dynamical systems. Springer, 2014.

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Cheban, David N. Global Attractors of Non-Autonomous Dynamical and Control Systems. World Scientific Publishing Co Pte Ltd, 2014.

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Cheban, David N. Global Attractors Of Non-autonomous Dissipative Dynamical Systems (Interdisciplinary Mathematical Sciences). World Scientific Publishing Company, 2004.

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William H, Boothby. Weapons and the Law of Armed Conflict. Oxford University Press, 2016. http://dx.doi.org/10.1093/law/9780198728504.001.0001.

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This book brings the legal rules governing the use of weapons in armed conflict together into a single volume and interprets and applies those principles and rules to particular weapons technologies. It is the essential reference book for anyone dealing or concerned with the international law applying to weaponry. After relating the historical evolution of weapons law, identifying its sources and discussing the important customary principles that are the foundation of the subject, the book explains to the reader in a logical sequence of chapters how treaty and customary rules apply to particular categories of weapon or to relevant technologies, both traditional and novel. Having explained to the reader how the existing law applies across the full range of weapons technologies, the book discusses how this dynamic field of international law may be expected to develop in the years ahead. This new edition tackles challenging weapons law issues such as the new treaty law on expanding bullets and on the arms trade, novel technologies in the fields of chemistry and biology, the topical controversies associated with autonomous and automated weapon systems, and how law applies to weapons in outer space and to cyber weapons. The law applicable in non-international armed conflicts is summarized; compliance and weapon reviews are carefully explained; and recent international and national military manuals, and other developments in the wider literature, are thoroughly reflected throughout the text.
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Book chapters on the topic "Non-autonomous dynamical systems"

1

Johnson, Russell, and Francesca Mantellini. "Non-Autonomous Differential Equations." In Dynamical Systems, 173–229. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-45204-1_3.

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Galor, Oded. "Higher-Order and Non-Autonomous Systems." In Discrete Dynamical Systems, 107–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/3-540-36776-4_5.

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Cánovas, Jose S. "On Entropy of Non–autonomous Discrete Systems." In Progress and Challenges in Dynamical Systems, 143–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38830-9_9.

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Mawhin, Jean. "Periodic Solutions of Non-autonomous Ordinary Differential Equations." In Mathematics of Complexity and Dynamical Systems, 1236–50. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1806-1_75.

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Zgurovsky, Michael Z., and Pavlo O. Kasyanov. "Uniform Global Attractors for Non-autonomous Dissipative Dynamical Systems." In Qualitative and Quantitative Analysis of Nonlinear Systems, 161–77. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59840-6_7.

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Ivanov, Anatoli F. "Global Asymptotic Stability in a Non-autonomous Difference Equation." In Difference Equations and Discrete Dynamical Systems with Applications, 231–50. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35502-9_10.

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Foti, Pilade, Aguinaldo Fraddosio, Salvatore Marzano, and Mario Daniele Piccioni. "Analysis of Non-autonomous Linear ODE Systems in Bifurcation Problems via Lie Group Geometric Numerical Integrators." In Dynamical Systems: Theoretical and Experimental Analysis, 97–111. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42408-8_9.

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Ribeiro, Fernando, Gil Lopes, Tiago Maia, Hélder Ribeiro, Pedro Osório, Ricardo Roriz, and Nuno Ferreira. "Motion Control of Mobile Autonomous Robots Using Non-linear Dynamical Systems Approach." In Lecture Notes in Electrical Engineering, 409–21. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43671-5_35.

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Nakamura, Yuichi, and Masahiro Nakagawa. "Approximation Capability of Continuous Time Recurrent Neural Networks for Non-autonomous Dynamical Systems." In Artificial Neural Networks – ICANN 2009, 593–602. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04277-5_60.

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Verichev, Nikolai, Stanislav Verichev, and Vladimir Erofeev. "Autonomous and Non-autonomous Systems with One Degree of Freedom." In Chaos, Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space, 1–24. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36103-7_1.

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Conference papers on the topic "Non-autonomous dynamical systems"

1

Kuo, Chi-Wei, and C. Steve Suh. "On Controlling Non-Autonomous Time-Delay Feedback Systems." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51128.

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Time-delay feedback oscillators of non-autonomous type are considered in the paper. These oscillators have been studied extensively for many decades in a broad set of fields such as sensor design, manufacturing, and machine dynamics. A time-delay model system having one time-delay constant and several nonlinear feedback terms in the governing differential equation is first studied. Many researches have demonstrated that a time-delay feedback even in the form of a small perturbation is able to perturb the oscillator to exhibit complex dynamical responses including bifurcation and route-to-chaos. These motions are harmful as they have a very negative impact on the stability, and thus output quality, of the system. For example, manufacturing processes that are characterized by time-delay feedback all have an operation limit on speed because the chaotic behaviors which are unpredictable and extremely unstable are difficult to control. With a viable control solution, the performance, quality, and capacity of manufacturing can be improved enormously. A novel concept capable of simultaneous control of vibration amplitude in the time-domain and spectral response in the frequency-domain has been demonstrated to be feasible for the control of dynamic instability including bifurcation and route-to-chaos in many nonlinear systems. The concept is followed to create a control configuration that is feasible for the mitigation of non-autonomous time-delay feedback oscillators. Featuring wavelet adaptive filters for simultaneous time-frequency resolution and filtered-x least mean square algorithm for online identification, the controller design is shown to successfully moderate the dynamic instability of the time-delay feedback oscillator and unconditionally warrant a limit cycle. The controller design that integrates all these features is able to mitigate dynamical deterioration in both the time and frequency domains and properly regulate the responses with the desired reference signal. Specifically the qualitative behavior of the controlled oscillator output follows a definitive fractal topology before settling into a stable manifold. The controlled response is categorically quasi-periodic and of the prescribed vibration amplitude and frequency spectrum. The control scheme is novel and requires no linearization. By applying wavelet domain analysis approach to the nonlinear control of instability, the true dynamics of the time-delay feedback system as delineated by both the time and frequency information are faithfully retained without being distorted or misinterpreted. Through employing adaptive technique, the high sensitivity of the time-delay feedback system to external disturbances is also properly addressed.
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Ma, Cuina, Peiyong Zhu, and Tianxiu Lu. "Some chaotic properties of non-autonomous discrete fuzzy dynamical systems." In 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2016. http://dx.doi.org/10.1109/fuzz-ieee.2016.7737666.

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Santos, C. M. P. "Generating timed trajectories for an autonomous vehicle: a non-linear dynamical systems approach." In IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004. IEEE, 2004. http://dx.doi.org/10.1109/robot.2004.1308849.

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Micó Ruiz, Juan Carlos. "Designing the mesoscopic approach of an autonomous linear dynamical system by a quantum formulation." In Systems & Design: Beyond Processes and Thinking. Valencia: Universitat Politècnica València, 2016. http://dx.doi.org/10.4995/ifdp.2016.2795.

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The work presents a mesoscopic approach to general systems modelled by dynamical systems. The quantum formulation is possible to be obtained by their quantum formulation from a second order Hamiltonian. However, only autonomous linear systems are proved to obtain a Hamiltonian like this. Some application cases are presented, and a discussion about how to generalize the formalism to non-linear dynamical systems is sketched.DOI: http://dx.doi.org/10.4995/IFDP.2016.2795
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Kuo, Chi-Wei, and C. Steve Suh. "The Optimization of Time-Frequency Control: Using Non-Autonomous Time-Delay Feedback Systems as Example." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-67170.

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A novel time-frequency nonlinear scheme demonstrated to be feasible for the control of dynamic instability including bifurcation, non-autonomous time-delay feedback oscillators, and route-to-chaos in many nonlinear systems is applied to the control of a time-delayed system. The control scheme features wavelet adaptive filters for simultaneous time-frequency resolution. Specifically Discrete Wavelet transform (DWT) is used to address the nonstationary nature of a chaotic system. The concept of active noise control is also adopted. The scheme applied the filter-x least mean square (FXLMS) algorithm which promotes convergence speed and increases performance. In the time-frequency control scheme, the FXLMS algorithm is modified by adding an adaptive filter to identify the system in real-time in order to construct a wavelet-based time-frequency controller capable of parallel on-line modeling. The scheme of such a construct, which possesses joint time-frequency resolution and embodies on-line FXLMS, is able to control non-autonomous, nonstationary system responses. Although the controller design is shown to successfully moderate the dynamic instability of the time-delay feedback oscillator and unconditionally warrant a limit cycle, parameters are required to be optimized. In this paper, the setting of the control parameters such as control time step, sampling rate, wavelet filter vector, and step size are studied and optimized to control a time-delay feedback oscillators of a nonautonomous type. The time-delayed oscillators have been applied in a broad set of fields including sensor design, manufacturing, and machine dynamics, but they can be easily perturbed to exhibit complex dynamical responses even with a small perturbation from the time-delay feedback. These responses for the system have a very negative impact on the stability, and thus output quality. Through employingfrequency-time control technique, the time responses of the time-delay feedback system to external disturbances are properly mitigated and the frequency responses are also suppressed, thus rendering the controlled responses quasi-periodic.
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Zhang, Wei, and Jun-Hua Zhang. "The Extended Melnikov Method for Non-Autonomous Higher Dimensional Nonlinear Systems and Multi-Pulse Chaotic Dynamics of Laminated Composite Piezoelectric Plate." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86154.

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The global bifurcations and multi-pulse chaotic dynamics of a simply supported laminated composite piezoelectric rectangular thin plate under combined parametric and transverse excitations are investigated in this paper for the first time. The formulas of the laminated composite piezoelectric rectangular plate are derived by using the von Karman-type equation, the Reddy’s third-order shear deformation plate theory and the Galerkin’s approach. The extended Melnikov method is improved to enable us to analyze directly the non-autonomous nonlinear dynamical system, which is applied to the non-autonomous governing equations of motion for the laminated composite piezoelectric rectangular thin plate. The results obtained here indicate that the multi-pulse chaotic motions can occur in the laminated composite piezoelectric rectangular thin plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the laminated composite piezoelectric rectangular thin plate.
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Insperger, Tamás, Gábor Stépán, and Sri N. Namachchivaya. "Comparison of the Dynamics of Low Immersion Milling and Cutting With Varying Spindle Speed." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21616.

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Abstract The stability properties of cutting processes are strongly limited by the so-called regenerative effect. This effect is originated in the presence of a time-delay in the dynamical system of the machine tool. This delay is inversely proportional to the cutting speed. Consequently, conventional cutting with a single-edge tool is modeled by an autonomous delay-differential equation (DDE). In case of milling, the varying number of cutting edges results in a kind of parametric excitation, and the corresponding mathematical model is a non-autonomous DDE. In case of low-immersion milling, this affects the stability boundaries in a substantial way. Cutting with varying spindle speed results non-autonomous DDEs where the time delay itself depends on the time periodically. A new semi-discretization method is proposed to handle the stability of these non-autonomous systems. The stability properties and corresponding bifurcations are compared in the above different cases of machining.
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Zhang, Wei, Min Sun, Qian Wang, and Jianen Chen. "Subharmonic Orbits of Rectangular Thin Plate With Parametrically and Externally Excitations." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-85868.

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In this paper, the bifurcations of subharmonic orbits for a four-dimensional rectangular thin plate with parametrically and externally excitations is considered for the first time. The formulas of the rectangular thin plate are derived by using the von Karman-type equation, the Reddy’s third-order shear deformation plate theory and the Galerkin’s approach. The unperturbed system is composed of two independent planar Hamiltonian systems such that the unperturbed system has a family of periodic orbits. The problem addressed here is the determination of sufficient conditions for some of the periodic orbits to generate subharmonic orbits after periodic perturbations. Thus, based on periodic transformations and Poincaré map the subharmonic Melnikov method is improved to enable us to analyze directly the non-autonomous nonlinear dynamical system, which is applied to the non-autonomous governing equations of motion for the parametrically and externally excited rectangular thin plate. The results obtained here indicate that subharmonic motions can occur in the rectangular thin plate. The method succeeds in establishing the existence of subharmonics in perturbed Hamiltonian systems as well as in discussing their bifurcations. Numerical simulation is also employed to find the subharmonic motions of the parametrically and externally excited rectangular thin plate.
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Gupta, T. C., and K. Gupta. "Correlation of Parameters to Instability and Chaos of a Horizontal Flexible Rotor Ball Bearing System." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-95308.

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The higher order effects from ball bearing nonlinearities cause complex vibration characteristics in rotor ball bearing systems. The sources of nonlinearities are internal radial clearance, Hertzian contact forces between balls and races and varying compliance effect. The same authors in their earlier work have identified the sets of parameters corresponding to instability and chaos for a horizontal flexible rotor supported on deep groove ball bearing. To the best of author’s knowledge, there is not much work reported in the literature on the dynamic analysis for instability and chaos, which is based on energy functions and bearing loads. Extending the preceding research work in the present paper by using a typical set of parameters and specifications of rotor ball bearing system, a correlation of parameters to instability and chaos is attempted using different energy functions associated with the dynamical system. A generalized Timoshenko beam finite element formulation is used to model the flexible rotor shaft. To achieve the convergence of solution with smaller number of elements, shape functions are derived from the exact solutions of governing differential equations of Timoshenko beam element. The sources of excitation are rotating unbalance and parametric excitation due to varying compliance of ball bearing during motion. For the bearing used in the present paper, the ratio of these excitation frequencies comes out to be an irrational number. Therefore, the dynamic response would be quasi-periodic with time period equal to infinity. To extend the use of non-autonomous shooting method to derive quasi-periodic solution, the fixed point algorithm (FPA) proposed in the literature is used to deduce the time period for non-autonomous shooting algorithm. The shooting method otherwise is used only to derive periodic solutions. Thus the non-autonomous shooting method coupled with fixed point algorithm (FPA) is used to compute the quasi-periodic solution, which also gives the monodromy matrix. The eigenvalues of the monodromy matrix, called Floqoet multipliers, give information about instability. The chaotic nature of the dynamic response is established by the maximum value of Lyapunov exponent. Once the instability and chaos is confirmed based on computed values of Floquet multipliers and Lyapunov exponents, the nature of the work done (positive or negative) by different conservative and non-conservative forces and moments during motion are analyzed and the fundamental causes, which make the system response unstable and / or chaotic, are established.
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Miah, Suruz, Mostafa M. H. Fallah, Arian Y. Panah, and Davide Spinello. "Non-Autonomous Feedback Control for Area Coverage Problems With Time-Varying Risk." In ASME 2016 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/dscc2016-9669.

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Motivated by area coverage optimization problems with time varying risk densities, we propose a decentralized control law for a team of autonomous mobile agents in a two dimensional area such that their asymptotic configurations optimize a generalized non-autonomous coverage metric. The generalized non-autonomous coverage metric explicitly depends on a nonuniform time-varying measurable scalar field that is not directly controllable by agents. Several interesting scenarios emerge with time varying risk density. In this work, we consider the case of area surveillance against moving targets or external threats penetrating through the perimeter, and the case of environmental monitoring and intervention with deployment of mobile sensors in areas affected by penetration of substances governed by diffusion mechanisms, as for example oil in a marine environment. In the presence of time-varying risk density the coverage metric is non-autonomous as it includes a time varying component that does not depend on the evolution of the agents. Our non-autonomous feedback law accounts for the time-varying component through a term that vanishes when the risk eventually stops evolving. Optimality with respect to the induced non-autonomous coverage is proven in the framework of Barbalat’s lemma, and the performance is illustrated through simulation of the these two scenarios.
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