Relevant bibliographies by topics / Hopf’s bifurcation

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

Academic literature on the topic 'Hopf’s bifurcation'

Author: Grafiati
Published: 28 May 2022
Last updated: 31 July 2025

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Journal articles on the topic "Hopf’s bifurcation"

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Martín, J. C., and L. Mora. "$C^2$-perturbations of Hopf’s bifurcation points and homoclinic tangencies." Proceedings of the American Mathematical Society 128, no. 4 (1999): 1241–45. http://dx.doi.org/10.1090/s0002-9939-99-05106-0.

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Mesa, Fernando, German Correa Velez, and Jose Jose Barba Ortega. "Hopf bifurcation in the study of synchronous motor stability." Ciencia en Desarrollo 13, no. 1 (2022): 1–7. http://dx.doi.org/10.19053/01217488.v13.n1.2022.12650.

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 In this document the dynamic model of the synchronous motor is presented, which has a typical structure of Lienard-type systems, the theory of dynamic systems is used, especially bifurcations, in this case, Hopf’s, which will be applied to the described model, to show the variations in the balance points of the system by taking the voltage of the bus to which it is connected as a variable parameter.
 
 
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Ojeda Toro, Juan Carlos, Izabela Dobrosz-Gómez, and Miguel Ángel Gómez García. "Setting Safe Operation Conditions for Acetyl Chloride Hydrolysis through Dynamic Modelling and Bifurcation Analysis." Modelling and Simulation in Engineering 2023 (November 18, 2023): 1–19. http://dx.doi.org/10.1155/2023/9685811.

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Acetyl chloride hydrolysis is a highly sensitive exothermic reaction that has presented several industrial safety issues. In the present study, a multiparameter mathematical model, previously developed and applied to simulate the oscillatory thermal behavior of an experimental continuous stirred tank reactor, was used to determine the static/dynamic bifurcation behavior of this reactive system. The values predicted by the model showed good agreement with the experimental data reported in the literature. Full topological classification of its fixed points and iterative maps was obtained: unique
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Nikolov, Svetoslav, and Valentin Nedev. "Bifurcation Analysis and Dynamic Behaviour of an Inverted Pendulum with Bounded Control." Journal of Theoretical and Applied Mechanics 46, no. 1 (2016): 17–32. http://dx.doi.org/10.1515/jtam-2016-0002.

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Abstract This paper presents an investigation on the behaviour of con- ventional inverted pendulum with an inertia disk in its free extreme. The system is actuated by means of torques applied to the disk by a DC mo- tor, mounted on the pendulum’s arm. Thus, the system is underactuated since the pendulum can rotate freely around its pivot point. The dynam- ical model is given with three ordinary nonlinear differential equations. Using Poincare-Andronov-Hopf’s theory, we find a new analytical formula for the first Lyapunov’s value at the boundary of stability. It enables one to study in detail t
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Bouachir, Amel, Mahmoud Mamou, Redha Rebhi, and Smail Benissaad. "Linear and Nonlinear Stability Analyses of Double-Diffusive Convection in a Vertical Brinkman Porous Enclosure under Soret and Dufour Effects." Fluids 6, no. 8 (2021): 292. http://dx.doi.org/10.3390/fluids6080292.

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Analytical and numerical investigations were performed to study the influence of the Soret and Dufour effects on double-diffusive convection in a vertical porous layer filled with a binary mixture and subject to horizontal thermal and solute gradients. In particular, the study was focused on the effect of Soret and Dufour diffusion on bifurcation types from the rest state toward steady convective state, and then toward oscillatory convective state. The Brinkman-extended Darcy model and the Boussinesq approximation were employed to model the convective flow within the porous layer. Following pa
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Xu, Chaoqun, and Sanling Yuan. "Spatial Periodic Solutions in a Delayed Diffusive Predator–Prey Model with Herd Behavior." International Journal of Bifurcation and Chaos 25, no. 11 (2015): 1550155. http://dx.doi.org/10.1142/s0218127415501552.

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A delayed diffusive predator–prey model with herd behavior subject to Neumann boundary conditions is studied both theoretically and numerically. Applying Hopf bifurcation analysis, we obtain the critical conditions under which the model generates spatially nonhomogeneous bifurcating periodic solutions. It is shown that the spatially homogeneous Hopf bifurcations always exist and that the spatially nonhomogeneous Hopf bifurcations will arise when the diffusion coefficients are suitably small. The explicit formulae for determining the direction of Hopf bifurcation and the stability of the bifurc
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Li, Wei, Chunrui Zhang, and Mi Wang. "Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges." Discrete Dynamics in Nature and Society 2024 (May 11, 2024): 1–18. http://dx.doi.org/10.1155/2024/9185585.

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This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidence
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Xu, Changjin. "Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters." Abstract and Applied Analysis 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/264870.

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A class of stage-structured predator-prey model with time delay and delay-dependent parameters is considered. Its linear stability is investigated and Hopf bifurcation is demonstrated. Using normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained. Finally, numerical simulations are performed to verify the analytical results.
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Yan, Xiang-Ping, and Wan-Tong Li. "Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays." Discrete Dynamics in Nature and Society 2006 (2006): 1–18. http://dx.doi.org/10.1155/ddns/2006/57254.

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We consider a simplified bidirectional associated memory (BAM) neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.
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Xu, Changjin, Maoxin Liao, and Xiaofei He. "Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays." International Journal of Applied Mathematics and Computer Science 21, no. 1 (2011): 97–107. http://dx.doi.org/10.2478/v10006-011-0007-0.

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Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations
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Dissertations / Theses on the topic "Hopf’s bifurcation"

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Коломієць, Світлана Володимирівна, Светлана Владимировна Коломиец та Svitlana Volodymyrivna Kolomiiets. "Дослідження біфуркації в напівкласичних моделях твердотільних лазерів". Thesis, Київський національний університет ім. Тараса Шевченка, 2003. http://essuir.sumdu.edu.ua/handle/123456789/62581.

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Динаміка напівкласичної моделі твердотільного лазера вивчається методом біфуркації ініціації циклу та отримані критерії стійкості граничних циклів, що відбуваються внаслідок біфуркації Хопфа, інтервали стійкості для параметр накачки, коли стаціонарний розчин розглядається як додатковий параметр. Метод Джозефа використовується для інтеграції системи чотирьох диференціальних рівнянь, які асимптотично описують динаміку лазерної моделі. За допомогою скорочення чотиривимірні завдання до двовимірного, ми знаходимо періодичне рішення системи диференціальних рівнянь.
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Fujihira, Takeo. "Hamiltonian Hopf bifurcation with symmetry." Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444087.

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Salih, Rizgar Haji. "Hopf bifurcation and centre bifurcation in three dimensional Lotka-Volterra systems." Thesis, University of Plymouth, 2015. http://hdl.handle.net/10026.1/3504.

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This thesis presents a study of the centre bifurcation and chaotic behaviour of three dimensional Lotka-Volterra systems. In two dimensional systems, Christopher (2005) considered a simple computational approach to estimate the cyclicity bifurcating from the centre. We generalized the technique to estimate the cyclicity of the centre in three dimensional systems. A lower bounds is given for the cyclicity of a hopf point in the three dimensional Lotka-Volterra systems via centre bifurcations. Sufficient conditions for the existence of a centre are obtained via the Darboux method using inverse J
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Harlim, John. "Codimension three Hopf and cusp bifurcation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ58343.pdf.

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Arakawa, Vinicius Augusto Takahashi. "Um estudo de bifurcações de codimensão dois de campos de vetores /." São José do Rio Preto : [s.n.], 2008. http://hdl.handle.net/11449/94243.

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Orientador: Claudio Aguinaldo Buzzi<br>Banca: João Carlos da Rocha Medrado<br>Banca: Luciana de Fátima Martins<br>Resumo: Nesse trabalho são apresentados alguns resultados importantes sobre bifurcações de codimensão dois de campos de vetores. O resultado principal dessa dissertação e o teorema que d a o diagrama de bifurcação e os retratos de fase da Bifurcação de Bogdanov-Takens. Para a demonstracão são usadas algumas técnicas basicas de Sistemas Dinâmicos e Teoria das Singularidades, tais como Integrais Abelianas, desdobramentos de Sistemas Hamiltonianos, desdobramentos versais, Teorema de P
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Arakawa, Vinicius Augusto Takahashi [UNESP]. "Um estudo de bifurcações de codimensão dois de campos de vetores." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/94243.

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Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-29Bitstream added on 2014-06-13T20:55:43Z : No. of bitstreams: 1 arakawa_vat_me_sjrp.pdf: 795168 bytes, checksum: 1ce40af6d71942f94c4c2bb678ce986f (MD5)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Nesse trabalho são apresentados alguns resultados importantes sobre bifurcações de codimensão dois de campos de vetores. O resultado principal dessa dissertação e o teorema que d a o diagrama de bifurcação e os retratos de fase da Bifurcação de Bogdanov-Takens. Para a de
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Pacha, Andújar Juan Ramón. "On the quasiperiodic hamiltonian andronov-hopf bifurcation." Doctoral thesis, Universitat Politècnica de Catalunya, 2002. http://hdl.handle.net/10803/5830.

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Aquest treball es situa dintre del marc dels sistemes dinàmics hamiltonians de tres graus de llibertat. Allà considerem famílies d'òrbites periòdiques amb una transició estable-complex inestable: sigui L el paràmetre que descriu la família i suposarem que per a valors del paràmetre més petits que un cert valor crític, L', els multiplicadors característics de les òrbites periòdiques corresponents hi són sobre el cercle unitat, quan L=L' aquests col·lisionen per parelles conjugades (òrbita ressonant o crítica) i per L > L', abandonen el cercle unitat cap al pla complex (col·lisió de Krein amb s
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Lee, Yoon-Mee. "Hopf Bifurcation in a Parabolic Free Boundary Problem." DigitalCommons@USU, 1992. https://digitalcommons.usu.edu/etd/7138.

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We deal with a free boundary problem for a nonlinear parabolic equation, which includes a parameter in the free boundary condition. This type of system has been used in models of ecological systems, in chemical reactor theory and other kinds of propagation phenomena involving reactions and diffusion. The main purpose of this dissertation is to show the global existence, uniqueness of solutions and that a Hopf bifurcation occurs at a critical value of the parameter r. The existence and uniqueness of the solution for this problem are shown by finding an equivalent regular free boundary problem t
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Silva, Dias Ana Paula da. "Bifurcations with wreath product symmetry." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302657.

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Bateman, Craig A. "Hopf bifurcation analysis for depth control of submersible vehicles." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1993. http://handle.dtic.mil/100.2/ADA276213.

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Books on the topic "Hopf’s bifurcation"

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van der Meer, Jan-Cees. The Hamiltonian Hopf Bifurcation. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0080357.

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Goodrich, John W. Hopf bifurcation in the driven cavity. NASA, 1989.

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E, Gustafson Karl, Halasi Kadosa, United States. National Aeronautics and Space Administration., and Lewis Research Center. Institute for Computational Mechanics in Propulsion., eds. Hopf bifurcation in the driven cavity. NASA, 1989.

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G, Chen, ed. Hopf bifurcation analysis: A frequency domain approach. World Scientific, 1996.

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Oral, Zeki Okan. Hopf bifurcations in path control of marine vehicles. Naval Postgraduate School, 1993.

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Dellnitz, Michael. Hopf-Verzweigung in Systemen mit Symmetrie und deren numerische Behandlung. Verlag an der Lottbek, 1989.

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Fiedler, Bernold. Global bifurcation of periodic solutions with symmetry. Springer-Verlag, 1988.

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Magal, Pierre. Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models. American Mathematical Society, 2009.

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1963-, Ruan Shigui, ed. Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models. American Mathematical Society, 2009.

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Jan Cornelis van der Meer. Hamiltonian Hopf Bifurcation. Springer London, Limited, 2006.

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Book chapters on the topic "Hopf’s bifurcation"

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Iooss, Gérard, and Daniel D. Joseph. "Secondary Subharmonic and Asymptotically Quasi-Periodic Bifurcation of Periodic Solutions (of Hopf’s Type) in the Autonomous Case." In Undergraduate Texts in Mathematics. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-0997-3_11.

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Smith, Hal. "Hopf Bifurcation." In An Introduction to Delay Differential Equations with Applications to the Life Sciences. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7646-8_6.

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Diekmann, Odo, Sjoerd M. Verduyn Lunel, Stephan A. van Gils, and Hanns-Otto Walther. "Hopf bifurcation." In Applied Mathematical Sciences. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4206-2_11.

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Sun, Xiaojuan. "Hopf Bifurcation." In Encyclopedia of Systems Biology. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_531.

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Chen, Yushu, and Andrew Y. T. Leung. "Hopf Bifurcation." In Bifurcation and Chaos in Engineering. Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-1575-5_6.

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Misbah, Chaouqi. "Hopf Bifurcation." In Complex Dynamics and Morphogenesis. Springer Netherlands, 2016. http://dx.doi.org/10.1007/978-94-024-1020-4_5.

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Börgers, Christoph. "Hopf Bifurcations." In An Introduction to Modeling Neuronal Dynamics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51171-9_13.

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Wu, Jianhong. "Hopf Bifurcations." In Theory and Applications of Partial Functional Differential Equations. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-4050-1_7.

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Liebscher, Stefan. "Zero-Hopf Bifurcation." In Bifurcation without Parameters. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10777-6_11.

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Liebscher, Stefan. "Double-Hopf Bifurcation." In Bifurcation without Parameters. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10777-6_12.

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Conference papers on the topic "Hopf’s bifurcation"

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Lin, Guojian, Balakumar Balachandran, and Eyad H. Abed. "Bifurcation Behavior of a Supercavitating Vehicle." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14052.

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In this effort, a numerical study of the bifurcation behavior of a supercavitating vehicle is conducted. The nonsmoothness of this system is due to the planing force acting on the vehicle. With a focus on dive-plane dynamics, bifurcations with respect to a quasi-static variation of the cavitation number are studied. The system is found to exhibit rich and complex dynamics including nonsmooth bifurcations such as the grazing bifurcation and smooth bifurcations such as Hopf bifurcations, cyclic-fold bifurcations, and period-doubling bifurcations, chaotic attractors, transient chaotic motions, an
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Ikeda, Takashi. "Bifurcation Phenomena Caused by Two Nonlinear Dynamic Absorbers." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34714.

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The characteristics of two nonlinear vibration absorbers simultaneously attached to structures under harmonic excitation are investigated. The frequency response curves are theoretically determined using van der Pol’s method. It is found from the theoretical analysis that pitchfork bifurcations may appear on a part of the response curves which are stable in a system with one nonlinear dynamic absorber. Three steady-state solutions with different amplitudes appear just after the pitchfork bifurcation. After that, Hopf bifurcations may occur depending on the values of the system parameters, and
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Cadou, Jean-Marc, Yann Guevel, and Gregory Girault. "Stability Analysis of 2D Flows by Numerical Tools Based on the Asymptotic Numerical Method: Application to the One and Two Sides Lid Driven Cavity." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82446.

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This work deals with the complete stability analysis in the case of two dimensional fluid flows searching for steady and Hopf bifurcations. The stability analysis starts with the computation of steady bifurcations. It is realized by first considering the monitoring of an indicator which is a scalar function. The indicator is computed via a perturbation method: the Asymptotic Numerical Method. Steady bifurcation point corresponds to the zero of this indicator. From this singular point, all the steady bifurcated branches are computed by using the perturbation method. Then the stability analysis
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Liao, Fulin, Jianliang Huang, and Weidong Zhu. "Analyzing Bifurcations of a Three-Degree-of-Freedom Gear Transmission Considering Multi-Piecewise Linear Functions." In ASME 2024 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/detc2024-144973.

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Abstract Bifurcations of a gear transmission system subjected to forced excitations considering multi-piecewise linear functions are investigated in this work by using the incremental harmonic balance (IHB) method. The nonlinear motion ordinary differential equations of the gear transmission system are formulated by employing the Newton’s second law. Analytical results reveal abundant bifurcation phenomena, including period-doubling bifurcations, saddle-node bifurcations, and Hopf bifurcations, which have not been exhibited in existing investigations on nonlinear behaviors of the gear transmis
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Wang, Yuefang, Lefeng Lu¨, and Yingxi Liu. "On Multiple Hopf Bifurcations of Airflow Excited Vibration of a Translating String." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34451.

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This paper presents the stability and bifurcation of transverse motion of translating strings excited by a steady wind flowfield. The stability of the equilibrium configuration is presented for loss of stability and generation of limit cycles via the Hopf bifurcation. It is demonstrated that there are single, double and quadruple Hopf bifurcations in the parametric space that lead to the limit cycle motion. The method of Incremental Harmonic Balance is used to solve the limit cycle response of which the stability is determined by computation of the Floquet multipliers. For the forced vibration
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Bajaj, Anil K., Joseph M. Johnson, and Seo Il Chang. "Amplitude Dynamics of an Autoparametric Two Degree-of-Freedom System." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0326.

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Abstract Forced, weakly nonlinear oscillations of a two degree-of-freedom autoparametric system are studied for resonant excitations. The method of averaging is used to obtain first order approximations to the response of the system. In the subharmonic case of internal and external resonance, where the external excitation is in the neighborhood of the higher natural frequency, a complete bifurcation analysis of the averaged equations is undertaken. The “locked pendulum” mode of response bifurcates to coupled-mode motion for some excitation frequencies and forcing amplitudes. The coupled-mode r
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Ikeda, Takashi. "Nonlinear Responses of Dual Pendulum Dynamic Absorbers." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86894.

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The nonlinear responses of a single-degree-of-freedom (SDOF) system with two pendulum tuned mass dampers (TMDs) under horizontal sinusoidal excitation are investigated. In the theoretical analysis, van der Pol’s method is applied to determine the expressions for the frequency response curves. In the numerical results, the differences between single- and dual-pendulum systems are shown. Pitchfork bifurcations occur followed by mode localization where both identical pendulums vibrate but at different amplitudes. Hopf bifurcations occur and then amplitude modulated motions including chaotic vibra
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Wu, Z. Q., and P. Yu. "Bifurcation Control of Ro¨ssler System." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-55035.

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In this paper, a new method is proposed for controlling bifurcations of nonlinear dynamical systems. This approach employs the idea used in deriving the transition variety sets of bifurcations with constraints to find the stability region of equilibrium points in parameter space. With this method, one can design, via a feedback control, appropriate parameter values to delay either static, or dynamic or both bifurcations as one wishes. The approach is applied to consider controlling bifurcations of the Ro¨ssler system. The uncontrolled Ro¨ssler has two equilibrium solutions, one of which exhibi
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Shukla, Amit, and Jeong Hoi Koo. "Control Bifurcations in a Nonlinear Active Suspension System for System Design." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-82374.

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Nonlinear active suspension systems are very popular in the automotive applications. They include nonlinear stiffness and nonlinear damping elements. One of the types of damping element is a magneto-rheological fluid based damper which is receiving increased attention in the applications to the automotive suspension systems. Latest trends in suspension systems also include electronically controlled systems which provide advanced system performance and integration with various processes to improve vehicle ride comfort, handling and stability. A control bifurcation of a nonlinear system typicall
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Yu, Bo, and Albert C. J. Luo. "Period Motions and Limit Cycle in a Periodically Forced, Plunged Galloping Oscillator." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67323.

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In this paper, periodic motions of a periodically forced, plunged galloping oscillator are investigated. The analytical solutions of stable and unstable periodic motions are obtained by the generalized harmonic balance method. Stability and bifurcations of the periodic motions are discussed through the eigenvalue analysis. The saddle-node and Hopf bifurcations of periodic motions are presented through frequency-amplitude curves. The Hopf bifurcation generates the quasiperiodic motions. Numerical simulations of stable and unstable periodic motions are illustrated.
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