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Relevant bibliographies by topics / Center manifold theory

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Academic literature on the topic 'Center manifold theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Center manifold theory"

1

Kashyap, Ankur, Willy Govaerts, Debasish Bhattacharjee, and Hemanta Sarmah. "Bifurcation analysis of a predator-prey system with density dependent disease recovery." Filomat 36, no. 20 (2022): 6897–922. http://dx.doi.org/10.2298/fil2220897k.

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The center manifold is an invariant manifold that plays a crucial role in the bifurcation analysis of dynamical systems. The center manifold existence theorem assures the local existence of an invariant submanifold of the state space of a dynamical system around a non-hyperbolic equilibrium point. Center manifold theory is essential in the reduction of different bifurcation scenarios to their normal forms. Our study focuses on a predator-prey interactive system with density-dependent growth in predators subject to a contagious disease. The disease is assumed to be horizontally transmitted, and

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Djellit, Ilham, and Baya Laadjal. "Center manifold in continuous time systems and computation." Facta universitatis - series: Electronics and Energetics 15, no. 3 (2002): 429–49. http://dx.doi.org/10.2298/fuee0203429d.

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The objective in this paper is to give some results of bifurcation equations, is concerned with the bifurcation from an equilibrium point in the case when the linear approximation has eigenvalues with zero real parts As we know, there is an intimate relationship between changes of stability and bifurcation. We formulate the main theorems that allow one to reduce dimension of a given system near a local bifurcation. We treat only continuous case. Center manifold theory is a method which uses power series expansions in the neighborhood of an equilibrium point in order to reduce the dimension of

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Boxler, Petra. "A stochastic version of center manifold theory." Probability Theory and Related Fields 83, no. 4 (1989): 509–45. http://dx.doi.org/10.1007/bf01845701.

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Kristiansen, K. Uldall. "Revisiting the Kepler problem with linear drag using the blowup method and normal form theory." Nonlinearity 37, no. 3 (2024): 035014. http://dx.doi.org/10.1088/1361-6544/ad2379.

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Abstract In this paper, we revisit the Kepler problem with linear drag. With dissipation, the energy and the angular momentum are both decreasing, but in Margheri et al (2017 Celest. Mech. Dyn. Astron. 127 35–48) it was shown that the eccentricity vector has a well-defined limit in the case of linear drag. This limiting eccentricity vector defines a conserved quantity, and in the present paper, we prove that the corresponding invariant sets are smooth manifolds. These results rely on normal form theory and a blowup transformation, which reveals that the invariant manifolds are (nonhyperbolic)

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Bersani, A. M., A. Borri, A. Milanesi, and P. Vellucci. "Tihonov theory and center manifolds for inhibitory mechanisms in enzyme kinetics." Communications in Applied and Industrial Mathematics 8, no. 1 (2017): 81–102. http://dx.doi.org/10.1515/caim-2017-0005.

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Abstract In this paper we study the chemical reaction of inhibition, determine the appropriate parameter ε for the application of Tihonov's Theorem, compute explicitly the equations of the center manifold of the system and find sufficient conditions to guarantee that in the phase space the curves which relate the behavior of the complexes to the substrates by means of the tQSSA are asymptotically equivalent to the center manifold of the system. Some numerical results are discussed.

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Cheng, Minquan, and Hsueh‐Chia Chang. "A generalized sideband stability theory via center manifold projection." Physics of Fluids A: Fluid Dynamics 2, no. 8 (1990): 1364–79. http://dx.doi.org/10.1063/1.857586.

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Kusakabe, Yuta. "An implicit function theorem for sprays and applications to Oka theory." International Journal of Mathematics 31, no. 09 (2020): 2050071. http://dx.doi.org/10.1142/s0129167x20500718.

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We solve fundamental problems in Oka theory by establishing an implicit function theorem for sprays. As the first application of our implicit function theorem, we obtain an elementary proof of the fact that approximation yields interpolation. This proof and Lárusson’s elementary proof of the converse give an elementary proof of the equivalence between approximation and interpolation. The second application concerns the Oka property of a blowup. We prove that the blowup of an algebraically Oka manifold along a smooth algebraic center is Oka. In the appendix, equivariantly Oka manifolds are char

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TURAEV, D. "ON DIMENSION OF NON-LOCAL BIFURCATIONAL PROBLEMS." International Journal of Bifurcation and Chaos 06, no. 05 (1996): 919–48. http://dx.doi.org/10.1142/s0218127496000515.

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An analogue of the center manifold theory is proposed for non-local bifurcations of homo- and heteroclinic contours. In contrast with the local bifurcation theory it is shown that the dimension of non-local bifurcational problems is determined by the three different integers: the geometrical dimension dg which is equal to the dimension of a non-local analogue of the center manifold, the critical dimension dc which is equal to the difference between the dimension of phase space and the sum of dimensions of leaves of associated strong-stable and strong-unstable foliations, and the Lyapunov dimen

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Beyer, P., R. Grauer, and K. H. Spatschek. "Center-manifold theory for low-frequency excitations in magnetized plasmas." Physical Review E 48, no. 6 (1993): 4665–73. http://dx.doi.org/10.1103/physreve.48.4665.

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Hupkes, H. J., and S. M. Verduyn Lunel. "Center Manifold Theory for Functional Differential Equations of Mixed Type." Journal of Dynamics and Differential Equations 19, no. 2 (2006): 497–560. http://dx.doi.org/10.1007/s10884-006-9055-9.

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Dissertations / Theses on the topic "Center manifold theory"

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Books on the topic "Center manifold theory"

1

Dumortier, Freddy. Canard cycles and center manifolds. American Mathematical Society, 1996.

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Gérard, Iooss, ed. Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems. Springer, 2011.

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editor, Donagi Ron, Douglas, Michael (Michael R.), editor, Kamenova Ljudmila 1978 editor, and Roček M. (Martin) editor, eds. String-Math 2013: Conference, June 17-21, 2013, Simons Center for Geometry and Physics, Stony Brook, NY. American Mathematical Society, 2014.

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Center for Mathematics at Notre Dame and American Mathematical Society, eds. Toplogy and field theories: Center for Mathematics at Notre Dame, Center for Mathematics at Notre Dame : summer school and conference, Topology and field theories, May 29-June 8, 2012, University of Notre Dame, Notre Dame, Indiana. American Mathematical Society, 2014.

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Carr, J. Applications of Centre Manifold Theory. Springer London, Limited, 2012.

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Iooss, Gérard, and Mariana Haragus. Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems. Springer, 2018.

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Cattani, Eduardo, and Phillip Griffiths. Introduction to Kähler Manifolds. Edited by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, et al. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161341.003.0001.

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This chapter provides an introduction to the basic results on the topology of compact Kähler manifolds that underlie and motivate Hodge theory. This chapter consists of five sections which correspond, roughly, to the five lectures in the course given during the Summer School at the International Centre for Theoretical Physics (ICTP). The five topics under discussion are: complex manifolds; differential forms on complex manifolds; symplectic, Hermitian, and Kähler structures; harmonic forms; and the cohomology of compact Kähler manifolds. There are also two appendices. The first collects some r

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Bernstein, Jeffrey A. Baruch Spinoza. Edinburgh University Press, 2018. http://dx.doi.org/10.3366/edinburgh/9781474423632.003.0022.

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There is currently a paucity of literature relating to Agamben’s philosophical treatment of Spinoza (Julie Klein, Dimitris Vardoulakis and Miguel Vatter being notable exceptions).1 There has certainly been no attempt to show how Agamben’s manifold references to the seventeenth-century Dutch-Jewish philosopher form a constellation in his thought. In this chapter, I will attempt to bring those references together under the categorial headings of (1) ‘Living in the Middle Voice’ and (2) ‘The Contemplative Life as Inoperativity’. I choose these categories because Agamben’s key concern (as I read h

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Grosser, Florian, and Nassima Sahraoui, eds. Heidegger in the Literary World. The Rowman & Littlefield Publishing Group, 2021. https://doi.org/10.5040/9798881813789.

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Within the vast reception history of Martin Heidegger’s philosophical thought poets, novelists, and playwrights have occupied a central place. This collection of essays opens up new perspectives by tracing the manifold, often surprising ways in which Heideggerian concepts, motifs, and concerns have been taken up in literary and poetic writing since the middle of the 20th century. In their contributions, scholars from the Americas, Asia, and Europe explore intellectual constellations between Heidegger and selected literary figures such as John Ashbery, Julia de Burgos, Paul Celan, Elfriede Jeli

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Barr, Rebecca Anne, Sylvie Kleiman-Lafton, and Sophie Vasset, eds. Bellies, bowels and entrails in the eighteenth century. Manchester University Press, 2018. http://dx.doi.org/10.7228/manchester/9781526127051.001.0001.

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This collection of essays seeks to complicate the notion of the supremacy of the brain as the key organ of the Enlightenment, by focusing on the workings of the bowels and viscera that obsessed writers and thinkers during the long eighteenth century. These inner organs and their mysterious processes of digestion acted as complicating counterpoints to politeness and modes of refined sociability, drawing attention to the deeper, more fundamental, workings of the self. In a form of ‘history from below’, the volume situates the period’s preoccupations with waste, dirt, and detritus within the cont

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Book chapters on the topic "Center manifold theory"

1

Mei, Zhen. "Center Manifold Theory." In Numerical Bifurcation Analysis for Reaction-Diffusion Equations. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04177-2_7.

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Vanderbauwhede, A., and G. Iooss. "Center Manifold Theory in Infinite Dimensions." In Dynamics Reported. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-61243-5_4.

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Oppo, Gian-Luca, and Antonio Politi. "Adiabatic Elimination for Laser Equations via Center Manifold Theory." In Coherence and Quantum Optics VI. Springer US, 1989. http://dx.doi.org/10.1007/978-1-4613-0847-8_151.

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Precup, Radu-Emil, Stefan Preitl, and Stefan Solyom. "Center Manifold Theory Approach to the Stability Analysis of Fuzzy Control Systems." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48774-3_44.

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Rand, Richard H., and Dieter Armbruster. "Center Manifolds." In Perturbation Methods, Bifurcation Theory and Computer Algebra. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-1060-3_2.

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Sideris, Thomas C. "Center Manifolds and Bifurcation Theory." In Atlantis Studies in Differential Equations. Atlantis Press, 2013. http://dx.doi.org/10.2991/978-94-6239-021-8_9.

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Church, Kevin E. M., and Xinzhi Liu. "Computational Aspects of Centre Manifolds." In Bifurcation Theory of Impulsive Dynamical Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-64533-5_6.

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Mielke, Alexander. "The linear theory." In Hamiltonian and Lagrangian Flows on Center Manifolds. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0097547.

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Church, Kevin E. M., and Xinzhi Liu. "Existence, Regularity and Invariance of Centre Manifolds." In Bifurcation Theory of Impulsive Dynamical Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-64533-5_5.

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Böhmer, Klaus. "On Hybrid Methods for Bifurcation and Center Manifolds for General Operators." In Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56589-2_4.

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Conference papers on the topic "Center manifold theory"

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Khajepour, Amir, Farid Golnaraghi, and K. A. Morris. "Vibration Suppression of a Flexible Beam Using Center Manifold Theory." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0288.

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Abstract In this paper we develop a nonlinear control strategy based on modal coupling using the center manifold theory. As an example we use the technique for vibration suppression of a flexible beam. The controller in this case is a mass-spring-dashpot mechanism which is free to slide along the beam. The equations of the plant/controller are coupled and nonlinear, and the linearized equations of the system have two uncontrollable modes. As a result, the performance of the system can not be improved by linear control theory or by most conventional nonlinear control techniques. We use the norm

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Kasnakoglu, Cosku, and Andrea Serrani. "Analysis and Nonlinear Control of Galerkin Models Using Averaging and Center Manifold Theory." In 2007 American Control Conference. IEEE, 2007. http://dx.doi.org/10.1109/acc.2007.4282236.

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Wang Chao, Zhang Yao, and Wu ZhiGang. "Application of center manifold theory on analysis of voltage stability of single-machine infinite system with dynamic loads." In 7th IET International Conference on Advances in Power System Control, Operation and Management (APSCOM 2006). IEE, 2006. http://dx.doi.org/10.1049/cp:20062098.

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Wang, Deshi, Renbin Xiao, and Ming Yang. "The Attitude Stability for Longitudinal Motion of Underwater Vehicle." 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-21607.

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Abstract Although the equations describing the longitudinal motions of underwater vehicles are typically nonlinear, the linearized equations are still employed to design the depth controller by the traditional analysis methods in engineering for the sake of simplicity. The reduction of the nonlinearity loses the dynamics near the singular points, which may be responsible for the sudden climb or dive. The nonlinear systems limited in the longitudinal plane of the underwater vehicles are analyzed on center manifold through the bifurcation theory. It focuses on the case that single zero root in J

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Chen, Zhen, and Pei Yu. "Double-Hopf Bifurcation in an Oscillator With External Forcing and Time-Delayed Feedback Control." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85549.

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In this paper an oscillator with time delayed velocity feedback controls is studied in detail. The particular attention is focused on internal double-Hopf bifurcation with an external exciting force. Linear analysis is used to find the critical conditions under which a double-Hopf bifurcation occurs. Then center manifold theory is applied to obtain an ODE system described on a four-dimensional center manifold. Further, the technique of multiple-time scales is employed to find the approximate solutions of periodic and quasi-periodic motions. Finally, numerical simulation results are presented t

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Sinha, S. C., Sangram Redkar, Eric A. Butcher, and Venkatesh Deshmukh. "Order Reduction of Nonlinear Time Periodic Systems Using Invariant Manifolds." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48445.

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The basic problem of order reduction of linear and nonlinear systems with time periodic coefficients is considered. First, the equations of motion are transformed using the Lyapunov-Floquet transformation such that the linear parts of new set of equations are time invariant. At this stage, the linear order reduction technique can be applied in a straightforward manner. A nonlinear order reduction methodology is also suggested through a generalization of the invariant manifold technique via Time Periodic Center Manifold Theory. A ‘reducibility condition’ is derived to provide conditions under w

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Wei, Heng, Jian-Wei Lu, Hang-Yu Lu, and Sheng-Yong Ye. "Bifurcation Characteristic and Energy Transfer of Vehicle Shimmy System Considering the Coupling of Vertical and Lateral Dynamics." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-66827.

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Abstract Since the vehicle is a complex mechanical system with many subsystems, the influence of the dynamic coupling between the subsystems of the vehicle on shimmy should be taken seriously. Therefore, a 12 degrees-of-freedom dynamic model of vehicle shimmy system with consideration of the dynamic coupling between the vertical motion and the lateral motion of the vehicle is established. In particular, the influence of the vertical load of the tire on the nonlinear cornering force is also considered. Then, the dynamic stability of the shimmy system is discussed with the help of the system eig

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Han, Congying, and Alexandre N. Pechev. "Time-Varying Nonlinear Designs for Underactuated Attitude Control With Two Reaction Wheels." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59387.

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Reaction wheels are commonly employed for high precisision and agile pointing in spacecraft. In this paper, we consider the realization of three-axis stabilization with only two reaction wheels installed along two principle axes. In practise, the total angular momentum of the whole spacecraft periodically varies with time because of the existence of in-orbit disturbances. With regard to the time varying system, firstly, a time varying control law is presented for velocity dumping based on center manifold theory. Then a continuous nonlinear feedback controller with a periodic time varying term

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Onawola, Oluseyi O., and S. C. Sinha. "Stabilization of Aeroelastic Instabilities of Panels Using Bifurcation Control With Piezoelectric Actuation." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47982.

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Aeroelastic instabilities of a panel may result in buckling (divergence) or flutter (Hopf bifurcation), when it is acted upon by induced aerodynamic and externally applied loads under supersonic/hypersonic environment in this paper. These instabilities are stabilized using nonlinear bifurcation control with piezoelectric actuation. The center manifold theory is used to extract subsystems which completely capture the bifurcation behavior of the original system near critical parameter values represented by sets of parametrised first-order differential equations with feedback control. The princip

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Sinou, Jean-Jacques, Fabrice Thouverez, Olivier Dereure, and Guy-Bernard Mazet. "Non-Linear Dynamics of a Complex Aircraft Brake System: Experimental and Theoretical Approaches." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48579.

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Stability and non-linear dynamics in a complex aircraft brake model are investigated. The non-linear contact between the rotors ands the stators, and mechanisms between components of the brake system are considered. The stability analysis is performed by determining the eigenvalues of the jacobian matrix of the linearized system at the equilibrium point. Parametric studies with linear stability theory is conducted in order to determine the effect of system parameters on stability. In order to obtain time-history responses, the complete set of nonlinear dynamic equations may be integrated numer

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