Dissertations / Theses on the topic 'Bifurcation'
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Henderson, Michael E. Keller Herbert Bishop Keller Herbert Bishop. "Complex bifurcation /." Diss., Pasadena, Calif. : California Institute of Technology, 1985. http://resolver.caltech.edu/CaltechETD:etd-03262008-112516.
Full textSalih, 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.
Full textBinks, Douglas John. "Bifurcation phenomena in nematodynamics." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306928.
Full textTaverner, S. "Bifurcation in physical systems." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375327.
Full textImpey, M. D. "Bifurcation in Lapwood convection." Thesis, University of Bristol, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234799.
Full textArakawa, 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.
Full textBanca: João Carlos da Rocha Medrado
Banca: Luciana de Fátima Martins
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 Preparação de Malgrange, entre outros. Outra importante bifurcação clássica apresentada e a Bifurca cão do tipo Hopf-Zero, quando a matriz Jacobiana possui um autovalor simples nulo e um par de autovalores imagin arios puros. Foram usadas algumas hipóteses que garantem propriedades de simetria do sistema, dentre elas, assumiuse que o sistema era revers vel. Assim como na Bifurcação de Bogdanov-Takens, foram apresentados o diagrama de bifurcao e os retratos de fase da Bifurcação Hopf-zero bifurcação reversível. As técnicas usadas para esse estudo foram a forma normal de Belitskii e o método do Blow-up polar.
Abstract: In this work is presented some important results about codimension two bifurcations of vector elds. The main result of this work is the theorem that gives the local bifurcation diagram and the phase portraits of the Bogdanov-Takens bifurcation. In order to give the proof, some classic tools in Dynamical System and Singularities Theory are used, such as Abelian Integral, versal deformation, Hamiltonian Systems, Malgrange Preparation Theorem, etc. Another classic bifurcation phenomena, known as the Hopf-Zero bifurcation, when the Jacobian matrix has a simple zero and a pair of purely imaginary eigenvalues, is presented. In here, is added the hypothesis that the system is reversible, which gives some symmetry in the problem. Like in Bogdanov-Takens bifurcation, the bifurcation diagram and the local phase portraits of the reversible Hopf-zero bifurcation were presented. The main techniques used are the Belitskii theory to nd a normal forms and the polar Blow-up method.
Mestre
Jones, Mark C. W. "The bifurcation and secondary bifurcation of capillary-gravity waves in the presence of symmetry." Thesis, University of Bath, 1986. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370986.
Full textGaunersdorfer, Andrea, Cars H. Hommes, and Florian O. O. Wagener. "Bifurcation routes to volatility clustering." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/522/1/document.pdf.
Full textSeries: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
Fujihira, Takeo. "Hamiltonian Hopf bifurcation with symmetry." Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444087.
Full textDuka, E. D. "Bifurcation problems in finite elasticity." Thesis, University of Nottingham, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384747.
Full textMelbourne, I. "Bifurcation problems with octahedral symmetry." Thesis, University of Warwick, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383295.
Full textGiacomoni, Jacques. "Problèmes non compacts et bifurcation." Paris 9, 1997. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1997PA090063.
Full textRavnås, Eirik. "Continuation and Bifurcation software in MATLAB." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-8954.
Full textThis article contains discussions of the algorithms used for the construction of the continuation software implemented in this thesis. The aim of the continuation was to be able to perform continuation of equilibria and periodic solutions originating from a Hopf bifurcation point. Algorithms for detection of simple branch points, folds, and Hopf bifurcation points have also been implemented. Some considerations are made with regard to optimization, and two schemes for mesh adaptation of periodic solutions based on moving mesh equations are suggested.
Feudel, Fred, Norbert Seehafer, and Olaf Schmidtmann. "Bifurcation phenomena of the magnetofluid equations." Universität Potsdam, 1995. http://opus.kobv.de/ubp/volltexte/2007/1358/.
Full textDu, Yimian. "Bifurcation analysis in chemical reaction network." Thesis, Imperial College London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.511282.
Full textHarlim, 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.
Full textWelsh, S. C. "Generalised topological degree and bifurcation theory." Thesis, University of Glasgow, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372419.
Full textBuchendorfer, Thomas. "Bifurcation properties of dynamic urban models." Thesis, Cranfield University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.360072.
Full textBougherara, Brahim. "Problèmes non-linéaires singuliers et bifurcation." Thesis, Pau, 2014. http://www.theses.fr/2014PAUU3012/document.
Full textThis thesis is concerned with the mathematical study of nonlinear partial differential equations. Precisely, we have investigated a class of nonlinear elliptic and parabolic problems with singular coefficients. This lack of regularity involves some difficulties which prevent the straight-orward application of classical methods of nonlinear analysis based on compactness results. In the proofs of the main results, we show how to overcome these difficulties. Precisely we adapt some well-known techniques together with the use of new methods. In this framework, an important step is to estimate accurately the solutions in order to apply the weak comparison principle, to use the regularity theory of parabolic and elliptic equations and to develop in a new context the analytic theory of global bifurcation. The thesis presents two independent parts. 1- In the first part (corresponding to Chapter I), we are interested by a nonlinear and singular parabolic equation involving the p-Laplacian operator. We established for this problem that for any non-negative initial datum chosen in a certain Lebeque space, there exists a local positive weak solution. For that we use some a priori bounds based on logarithmic Sobolev inequalities to get ultracontractivity of the associated semi-group. Additionaly, for a range of values of the singular coefficient, we prove the uniqueness of the solution and further regularity results. 2- In the second part (corresponding to Chapters II, III and IV of the thesis), we are concerned with the study of global bifurcation problems involving singular nonlinearities. We establish the existence of a piecewise analytic global path of solutions to these problems. For that we use crucially the analytic bifurcation theory introduced by Dancer (described in Chapter II of the thesis). In the frame of a class of semilinear elliptic problems involving a critical nonlinearity in two dimensions, we further prove that the piecewise analytic path of solutions admits asymptotically a singular solution (i.e. an unbounded solution), whose Morse index is infinite. As a consequence, this path admits a countable infinitely many “turning points” where the Morse index is increasing
Caron, Jean-François. "Phénomène de bifurcation en électro-élasticité." Lille 1, 1997. http://www.theses.fr/1997LIL10120.
Full textSammon, Michel P. "Bifurcation analyses of respiratory vagal reflexes." Case Western Reserve University School of Graduate Studies / OhioLINK, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=case1060098227.
Full textHachich, Mohamed. "Conditions de bifurcation dans les solides /." Cachan : Laboratoire de mécanique et technologie, 1994. http://catalogue.bnf.fr/ark:/12148/cb35813140w.
Full textKwok, Loong-Piu. "Viscous cross-waves: Stability and bifurcation." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184441.
Full textHima, Nikolin. "Bifurcation based mechanisms for elastic metainterfaces." Doctoral thesis, Università degli studi di Trento, 2022. https://hdl.handle.net/11572/362105.
Full textPacha, Andújar Juan Ramón. "On the quasiperiodic hamiltonian andronov-hopf bifurcation." Doctoral thesis, Universitat Politècnica de Catalunya, 2002. http://hdl.handle.net/10803/5830.
Full textNostre objectiu és entendre la dinàmica local en un entorn de l'òrbita periòdica ressonant per tal de provar, analíticament, l'existència dels tors invariants bifurcats segons l'esquema descrit dalt. Això el portem a terme mitjançant l'anàlisi següent:
(i) Primer de tot obtenim d'una manera constructiva (això és, donant algorismes) una forma normal ressonant en un entorn de l'òrbita periòdica crítica. Aquesta forma normal la portem fins a qualsevol ordre arbitrari r. Així doncs, mostrem que el hamiltonià inicial es pot posar com la suma de la forma normal (integrable) més una resta no integrable. A partir d'aquí, podem estudiar la dinàmica de la forma normal, prescindint dels altres termes i, amb aquest tractament (formal) del problema, som capaços d'identificar els paràmetres que governen tant l'existència de la bifurcació com la seva tipologia (directa, inversa). Cal, remarcar que el que es fa fins aquí, no és només un procés qualitatiu, ja que a més ens permet derivar parametritzacions molt acurades dels tors no pertorbats.
(ii) A continuació, calculem acotacions "òptimes" per a la resta. D'aquesta manera, esperem provar que un bon nombre de tors (en sentit de la mesura) es preserven quan s'afegeix la pertorbació.
(iii) Finalment, apliquem mètodes KAM per establir que la majoria (veure comentari dalt) dels tors bifurcats sobreviuen. Aquests mètodes es basen en la construcció d'un esquema de convergència quadràtica capaç de contrarestar l'efecte dels petits divisors que apareixen quan s'aplica teoria de pertorbacions per trobar solucions quasi-periòdiques. En el nostre cas, a més, resulta que alguna de les condicions "típiques" que s'imposen sobre les freqüències (intrínseques i normals) dels tors no pertorbats, no estan ben definides per als tors bifurcats, de manera que ens ha calgut desenvolupar un tractament més específic.
keywords: Bifurcation problems, perturbations, normal forms, small divisors, KAM theory.
Classificació AMS: 37J20, 37J25, 37J40
This work is placed into the context of the three-degree of freedom Hamiltonian systems, where we consider families of periodic orbits undergoing transitions stable-complex unstable. More precisely: Let L be the parameter of the family and assuming that, for values of L smaller than some critical value say, L', the characteristic multipliers of the periodic orbits lie on the unit circle, when L=L' they colllide pairwise (critical or resonant periodic orbit) and, for L > L' leave the unit circle towards the complex plane (Krein collision with opposite signature).
From numerical studies on some concrete symplectic maps (for instance, D. Pfennniger, Astron. Astrophys. 150, 97-111, 1985) it is known the rising (under certain irrationality conditions), of quasi-periodic bifurcation phenomena, in particular, the appearance of unfolded 2D invariant tori families. Moreover, the bifurcation takes place in a way that resembles the classical Andronov-Hopf one, in the sense that either stable invariant objects (elliptic tori) unfold "around" linear unstable periodic orbits, or conversely, unstable invariant structures (hyperbolic tori) appear "surrounding" stable periodic orbits.
Our objective is, thus, to understand the (local) dynamics in a neighbourhood of the critical periodic orbit well enough to prove analytically, the existence of such quasi-periodic solutions together with the bifurcation pattern described above. This is carried out through three steps:
(i) First, we derive, in a constructive way (i. e., giving algorithms), a resonant normal form around the critical periodic orbit up to any arbitrary order r. Whence, we show that the initial raw Hamiltonian can be casted --through a symplectic change--, into an integrable part, the normal form itself, plus a (non-integrable) remainder. From here, one can study the dynamics of the normal form, skipping the remainder off. As a result of this (formal) approach, we are able to indentify the parameters governing both, the presence of the bifurcation and its type (direct, inverse). We remark that this is not a merely qualitative process for, in addition, accurate parametrizations of the bifurcated families of invariant tori are derived in this way.
(ii) Beyond the formal approach, we compute "optimal" bounds for the remainder of the normal form, so one expects to prove the preservation of a higher (in the measure sense) number of invariant tori --than, indeed, with a less sharp estimates--.
(iii) Finally, we apply KAM methods to establish the persistence of (most, in the measure sense) of the bifurcated invariant tori. These methods involve the design of a suitable quadratic convergent scheme, able to overcome the effect of the small divisors appearing in perturbation techniques when one looks for quasi-periodic solutions. In this case though, some of the "typical" conditions that one imposes on the frequencies (intrinsic and normal) of the unperturbed invariant tori do not work, due to the proximity to parabolic tori, so one is bound to sketch specific tricks.
keywords: Bifurcation problems, perturbations, normal forms, small divisors, KAM theory
AMS classification: 37J20, 37J25, 37J40
Gemici, Omer Caner. "Numerical Bifurcation Analysis Of Cosymmetric Dynamical Systems." Thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1260425/index.pdf.
Full textSchumacher, Jörg, and Norbert Seehafer. "Bifurcation analysis of the plane sheet pinch." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2007/1492/.
Full textPark, Jungho. "Bifurcation and stability problems in fluid dynamics." [Bloomington, Ind.] : Indiana University, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3274924.
Full textSource: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4529. Adviser: Shouhong Wang. Title from dissertation home page (viewed Apr. 22, 2008).
Kwalik, Kristina Mary. "Bifurcation characteristics in closed-loop polymerization reactors." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/11711.
Full textAnayiotos, Andreas Stavrou. "Fluid dynamics at a compliant bifurcation model." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/12939.
Full textShen, Wenxian. "Staility and bifurcation of traveling wave solutions." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/29354.
Full textBaghdadi, Nadjib. "Bifurcation and continuation analysis : flexible aircraft dynamics." Thesis, University of Bristol, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.539769.
Full textTzanov, Vassil Vassilev. "Bifurcation analysis applied to inclined cable dynamics." Thesis, University of Bristol, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.606568.
Full text徐善強 and Sin-keung Chui. "Stability and bifurcation in flow induced vibration." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31235724.
Full textDavidson, Fordyce A. "Bifurcation in systems of reaction-diffusion equations." Thesis, Heriot-Watt University, 1993. http://hdl.handle.net/10399/1444.
Full textMcGarry, John Kevin. "Application of bifurcation theory to physical problems." Thesis, University of Leeds, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252925.
Full textTomlin, Alison Sarah. "Bifurcation analysis for non-linear chemical kinetics." Thesis, University of Leeds, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.255345.
Full textCharles, Guy Alexander. "Bifurcation tailoring applied to nonlinear flight dynamics." Thesis, University of Bristol, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274630.
Full textOrr, Anthony. "The eversion and bifurcation of elastic cylinders." Thesis, University of Glasgow, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307194.
Full textOPREA, PETRESCU IULIANA. "Bifurcation et evolution temporelle de dynamos convectives." Nice, 1994. http://www.theses.fr/1994NICE4787.
Full textLari-Lavassani, Ali. "Multiparameter bifurcation with symmetry via singularity theory /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487683049377079.
Full textKumeno, Hironori. "Bifurcation and Synchronization in Parametrically Forced Systems." Thesis, Toulouse, INSA, 2012. http://www.theses.fr/2012ISAT0024/document.
Full textIn this thesis, we propose a N-dimensional coupled discrete-time system whose parameters are forced into periodic varying, the N-dimensional system being constructed of n same one-dimensional subsystems with mutually influencing coupling and also coupled continuous-time system including periodically parameter varying which correspond to the periodic varying in the discrete-time system.Firstly, we introduce the N-dimensional coupled parametrically forced discrete-time system and its general properties. Then, when logistic maps is used as the one-dimensional subsystem constructing the system, bifurcations in the one or two-dimensional parametrically forced logistic map are investigated. Crossroad area centered at fold cusp points regarding several order cycles are confirmed.Next, we investigated behaviors of the coupled Chua's circuit whose parameter is forced into periodic varying associated with the period of an internal state value. From the investigation of bifurcations in the system, non-existence of odd order cycles and coexistence of different attractors are observed. From the investigation of synchronizations coexisting of many attractors whose synchronizations states are different are observed. Observed phenomena in the system is compared with the parametrically forced discrete-time system. Similar phenomena are confirmed between the parametrically forced discrete-time system and the parametrically forced Chua's circuit. It is worth noting that this facilitates to analyze parametrically forced continuous-time systems, because to analyze discrete-time systems is easier than continuous-time systems. Finally, we investigated behaviors of another coupled continuous-time system in which Chua's circuit is used, while, the motion of the switch controlling the parametric varying is different from the above system. Coexisting of many attractors whose synchronizations states are different are observed. Comparing with theabove system, the number of coexisting stable state is increased by the effect of the different switching motion
Chui, Sin-keung. "Stability and bifurcation in flow induced vibration /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1904155X.
Full textMeissen, Emily Philomena, and Emily Philomena Meissen. "Invading a Structured Population: A Bifurcation Approach." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/625610.
Full textGomez, Maria Gabriela Miranda. "Symmetries in bifurcation theory : the appropriate context." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/110618/.
Full textArakawa, 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.
Full textFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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 Preparação de Malgrange, entre outros. Outra importante bifurcação clássica apresentada e a Bifurca cão do tipo Hopf-Zero, quando a matriz Jacobiana possui um autovalor simples nulo e um par de autovalores imagin arios puros. Foram usadas algumas hipóteses que garantem propriedades de simetria do sistema, dentre elas, assumiuse que o sistema era revers vel. Assim como na Bifurcação de Bogdanov-Takens, foram apresentados o diagrama de bifurcao e os retratos de fase da Bifurcação Hopf-zero bifurcação reversível. As técnicas usadas para esse estudo foram a forma normal de Belitskii e o método do Blow-up polar.
In this work is presented some important results about codimension two bifurcations of vector elds. The main result of this work is the theorem that gives the local bifurcation diagram and the phase portraits of the Bogdanov-Takens bifurcation. In order to give the proof, some classic tools in Dynamical System and Singularities Theory are used, such as Abelian Integral, versal deformation, Hamiltonian Systems, Malgrange Preparation Theorem, etc. Another classic bifurcation phenomena, known as the Hopf-Zero bifurcation, when the Jacobian matrix has a simple zero and a pair of purely imaginary eigenvalues, is presented. In here, is added the hypothesis that the system is reversible, which gives some symmetry in the problem. Like in Bogdanov-Takens bifurcation, the bifurcation diagram and the local phase portraits of the reversible Hopf-zero bifurcation were presented. The main techniques used are the Belitskii theory to nd a normal forms and the polar Blow-up method.
Swat, Maciej J. "Bifurcation analysis of regulatory modules in cell biology." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=981033113.
Full textKorobeinikov, Andrei. "Stability and bifurcation of deterministic infectious disease models." Thesis, University of Auckland, 2001. http://wwwlib.umi.com/dissertations/fullcit/3015611.
Full textSubscription resource available via Digital Dissertations
Smith, Robert Frederick. "Geometric models of the stenosed human carotid bifurcation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ32510.pdf.
Full textVenkatagiri, Shankar C. "The peak-crossing bifurcation in lattice dynamical systems." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/29340.
Full text