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Academic literature on the topic 'Bifurcation problems'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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Journal articles on the topic "Bifurcation problems"

1

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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Chien, C. S., Z. Mei, and C. L. Shen. "Numerical Continuation at Double Bifurcation Points of a Reaction–Diffusion Problem." International Journal of Bifurcation and Chaos 08, no. 01 (1998): 117–39. http://dx.doi.org/10.1142/s0218127498000097.

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We study double bifurcations of a reaction–diffusion problem, and numerical methods for the continuation of bifurcating solution branches. To ensure a correct reflection of the bifurcation scenario in discretizations and to reduce imperfection of bifurcations, we consider a preservation of multiplicities of the bifurcation points in the discrete problems. A continuation-Arnoldi algorithm is exploited to trace the solution branches, and to detect secondary bifurcations. Numerical results on the Brusselator equations confirm our analysis.

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Postlethwaite, C. M., G. Brown, and M. Silber. "Feedback control of unstable periodic orbits in equivariant Hopf bifurcation problems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1999 (2013): 20120467. http://dx.doi.org/10.1098/rsta.2012.0467.

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Symmetry-breaking Hopf bifurcation problems arise naturally in studies of pattern formation. These equivariant Hopf bifurcations may generically result in multiple solution branches bifurcating simultaneously from a fully symmetric equilibrium state. The equivariant Hopf bifurcation theorem classifies these solution branches in terms of their symmetries, which may involve a combination of spatial transformations and temporal shifts. In this paper, we exploit these spatio-temporal symmetries to design non-invasive feedback controls to select and stabilize a targeted solution branch, in the even

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WU, ZHIQIANG, PEI YU, and KEQI WANG. "BIFURCATION ANALYSIS ON A SELF-EXCITED HYSTERETIC SYSTEM." International Journal of Bifurcation and Chaos 14, no. 08 (2004): 2825–42. http://dx.doi.org/10.1142/s0218127404010862.

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This paper investigates periodic bifurcation solutions of a mechanical system which involves a van der Pol type damping and a hysteretic damper representing restoring force. This system has recently been studied based on the singularity theory for bifurcations of smooth functions. However, the results do not actually take into account the property of nonsmoothness involved in the system. In particular, the transition varieties due to constraint boundaries were ignored, resulting in failure in finding some important bifurcation solutions. To reveal all possible bifurcation patterns for such sys

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Armbruster, D., and G. Dangelmayr. "Coupled stationary bifurcations in non-flux boundary value problems." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 1 (1987): 167–92. http://dx.doi.org/10.1017/s0305004100066500.

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AbstractCoupled stationary bifurcations in nonlinear operator equations for functions, which are defined on a real interval with non-flux boundary conditions at the ends, are analysed in the framework of imperfect bifurcation theory. The bifurcation equations resulting from a Lyapunov–Schmidt reduction possess a natural structure which can be obtained by taking real parts of a diagonal action in ℂ2 of the symmetry group 0(2). A complete unfolding theory is developed and bifurcation equations are classified up to codimension two. Structurally stable bifurcation diagrams are given and their depe

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Sridhar, Lakshmi N. "Elimination of oscillation causing Hopf bifurcations in engineering problems." Journal of AppliedMath 2, no. 5 (2024): 1826. http://dx.doi.org/10.59400/jam1826.

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Bifurcation analysis was performed on various engineering process problems that exhibit undesirable oscillation causing Hopf bifurcations. Hopf bifurcations result in oscillatory behavior which is problematic for optimization and control tasks. Additionally, the presence of oscillations causes a reduction in product quality and in some cases causes equipment damage. The hyperbolic tangent function activation factor is normally used in neural networks and optimal control problems to eliminate spikes in optimum profiles. Spikes are similar to oscillatory profiles and this is the motivation to in

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Cliffe, K. A., A. Spence, and S. J. Tavener. "The numerical analysis of bifurcation problems with application to fluid mechanics." Acta Numerica 9 (January 2000): 39–131. http://dx.doi.org/10.1017/s0962492900000398.

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In this review we discuss bifurcation theory in a Banach space setting using the singularity theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical analysis of bifurcation problems is discussed and the convergence theory for several important bifurcations is described for both projection and finite difference methods. These results are used to provide a convergence theory for the mixed finite element method applied to the steady incompressible Navier–Stokes equations. Numerical methods for the calculation of several common bifurcations are described and the

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Aydin Akgun, Fatma. "Global Bifurcation of Fourth-Order Nonlinear Eigenvalue Problems’ Solution." International Journal of Differential Equations 2021 (November 26, 2021): 1–6. http://dx.doi.org/10.1155/2021/7516324.

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In this paper, we study the global bifurcation of infinity of a class of nonlinear eigenvalue problems for fourth-order ordinary differential equations with nondifferentiable nonlinearity. We prove the existence of two families of unbounded continuance of solutions bifurcating at infinity and corresponding to the usual nodal properties near bifurcation intervals.

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Neiman, Aleksander. "The cumulant approach for the investigation of bifurcations of dynamical systems driven by the external noise." Izvestiya VUZ. Applied Nonlinear Dynamics 3, no. 3 (1995): 8–21. https://doi.org/10.18500/0869-6632-1995-3-3-8-21.

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The problems of bifurcation analysis of noisy systems are considered. The technique of bifurcation analysis based on the cumulant expansion is proposed. The noise influence оn the mode-lockirg bifurcations in the circle map and оn the period-doubling bifurcations in the Feigenbaum map is considered as examples.

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Deng, Baoyang, Michael O'Connor, and Bill Goodwine. "Bifurcations and symmetry in two optimal formation control problems for mobile robotic systems." Robotica 35, no. 8 (2016): 1712–31. http://dx.doi.org/10.1017/s026357471600045x.

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SUMMARYThis paper studies bifurcations in the solution structure of an optimal control problem for mobile robotic formation control. In particular, this paper studies a group of mobile robots operating in a two-dimensional environment. Each robot has a predefined initial state and final state and we compute an optimal path between the two states for every robot. The path is optimized with respect to two factors, the control effort and the deviation from a desired “formation,” and a bifurcation parameter gives the relative weight given to each factor. Using an asymptotic analysis, we show that

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Dissertations / Theses on the topic "Bifurcation problems"

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Duka, E. D. "Bifurcation problems in finite elasticity." Thesis, University of Nottingham, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384747.

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Melbourne, I. "Bifurcation problems with octahedral symmetry." Thesis, University of Warwick, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383295.

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Park, 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.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2007.<br>Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4529. Adviser: Shouhong Wang. Title from dissertation home page (viewed Apr. 22, 2008).

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McGarry, 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.

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Bougherara, Brahim. "Problèmes non-linéaires singuliers et bifurcation." Thesis, Pau, 2014. http://www.theses.fr/2014PAUU3012/document.

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Cette thèse s’inscrit dans le domaine mathématique de l’analyse des équations aux dérivées partielles non linéaires. Précisément, nous nous sommes intéressés à une classe de problèmes elliptiques et paraboliques avec coefficients singuliers. Ce manque de régularité pose un certain nombre de difficultés qui ne permettent pas d’utiliser directement les méthodes classiques de l’analyse non-linéaire fondées entre autres sur des résultats de compacité. Dans les démonstrations des principaux résultats, nous montrons comment pallier ces difficultés. Ceci suppose d’adapter certaines techniques bien co

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Manoel, Miriam Garcia. "Hidden symmetries in bifurcation problems : the singularity theory." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327556.

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Menon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." Thesis, The University of Sydney, 2008. http://hdl.handle.net/2123/3685.

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A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also

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Menon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." University of Sydney, 2008. http://hdl.handle.net/2123/3685.

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Doctor of Philosophy<br>A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions t

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Sallam, M. H. M. "Aspects of stability and bifurcation theory for multiparameter problems." Thesis, University of Strathclyde, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371969.

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Zhang, Tiansi. "Problems of homoclinic flips bifurcation in four-dimensional systems." Lyon, École normale supérieure (sciences), 2007. http://www.theses.fr/2007ENSL0431.

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Books on the topic "Bifurcation problems"

1

Melbourne, Ian. Bifurcation problems with octahedral symmetry. typescript, 1987.

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2

Mittelmann, Hans D., and Dirk Roose, eds. Continuation Techniques and Bifurcation Problems. Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-5681-2.

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1945-, Mittelmann H. D., and Roose Dirk, eds. Continuation techniques and bifurcation problems. Birkhäuser Verlag, 1990.

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4

Fečkan, Michal. Topological Degree Approach to Bifurcation Problems. Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8724-0.

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5

Manoel, Míriam Garcia. Hidden symmetries in bifurcation problems: The singularity theory. typescript, 1997.

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6

Center, Langley Research, ed. Multigrid methods for bifurcation problems: The self adjoint case. National Aeronautics and Space Administration, Langley Research Center, 1987.

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7

Schaaf, Renate. Globalsolution branches of two point boundary value problems. Springer-Verlag, 1990.

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8

Doedel, Eusebius, and Laurette S. Tuckerman, eds. Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1208-9.

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9

Le, Vy Khoi. Global bifurcation invariational inequalities: Applications to obstacle and unilateral problems. Springer, 1997.

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Doedel, Eusebius. Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems. Springer New York, 2000.

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Book chapters on the topic "Bifurcation problems"

1

Gaeta, Giuseppe. "Bifurcation problems." In Nonlinear Symmetries and Nonlinear Equations. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1018-1_6.

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2

Luongo, Angelo, Manuel Ferretti, and Simona Di Nino. "Solved Problems." In Stability and Bifurcation of Structures. Springer International Publishing, 2012. http://dx.doi.org/10.1007/978-3-031-27572-2_14.

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3

Salvadori, L., and F. Visentin. "Stability and Bifurcation Problems." In Modern Methods of Analytical Mechanics and their Applications. Springer Vienna, 1998. http://dx.doi.org/10.1007/978-3-7091-2520-5_3.

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Mei, Zhen. "Bifurcation Problems with Symmetry." In Numerical Bifurcation Analysis for Reaction-Diffusion Equations. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04177-2_5.

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Ambrosetti, Antonio, and David Arcoya. "Bifurcation Theory." In An Introduction to Nonlinear Functional Analysis and Elliptic Problems. Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8114-2_6.

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6

Motreanu, Dumitru, Viorica Venera Motreanu, and Nikolaos Papageorgiou. "Bifurcation Theory." In Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_7.

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Allgower, E. L., C. S. Chien, and K. Georg. "Large sparse continuation problems." In Continuation Techniques and Bifurcation Problems. Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-5681-2_1.

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True, Hans. "Bifurcation Problems in Railway Vehicle Dynamics." In Bifurcation: Analysis, Algorithms, Applications. Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7241-6_33.

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Chow, Shui-Nee, and Reiner Lauterbach. "On Bifurcation for Variational Problems." In Dynamics of Infinite Dimensional Systems. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-86458-2_7.

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Mandel, Paul. "Bifurcation Problems in Nonlinear Optics." In Instabilities and Chaos in Quantum Optics II. Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2548-0_21.

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Conference papers on the topic "Bifurcation problems"

1

Ansari, Md Shabaz, Hemkant Nehete, Andrea Grimaldi, et al. "A comparison of Oscillatory Ising Machines and Simulated Bifurcation Machines for Solving Maximum Cut Problems." In 2024 IEEE 24th International Conference on Nanotechnology (NANO). IEEE, 2024. http://dx.doi.org/10.1109/nano61778.2024.10628622.

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LUCIA, MARCELLO, and MYTHILY RAMASWAMY. "GLOBAL BIFURCATION FOR SEMILINEAR ELLIPTIC PROBLEMS." In Proceedings of the International Conference on Nonlinear Analysis. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812709257_0013.

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Ji, Quanbao, Qishao Lu, and Xia Gu. "Computation of D10-Equivariant Nonlinear Bifurcation Problems." In 2009 Fifth International Conference on Natural Computation. IEEE, 2009. http://dx.doi.org/10.1109/icnc.2009.250.

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Ramuzat, A., H. Richard, and M. L. Riethmuller. "Unsteady Flows Within a 2D Model of Multiple Lung Bifurcations." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0363.

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Abstract In our environment, chronic pulmonary illness due to pollution effects or asthmatic problems are increasing. To identify the contribution of pollution effect on the alterations in breath patterns, a better understanding of the human pulmonary system is needed. As a result, fields to be investigated are mostly flows in the lungs at high breathing frequency and aerosol deposition in lung bifurcations under unsteady conditions. The respiration pattern has to be better understood and investigated, to have the possibility to get the most appropriate palliative treatment. Most of the medica

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Kolesnikov, Andrey Vitalievich. "Passionary Oscillator." In 7th International Conference “Futurity designing. Digital reality problems”. Keldysh Institute of Applied Mathematics, 2024. http://dx.doi.org/10.20948/future-2024-8-3.

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A one-dimensional nonlinear mapping is proposed that describes the dynamics of a passionary oscillator and is capable of transitioning to chaos through a series of period doubling bifurcations. Its dynamic behavior was studied and a bifurcation tree was constructed, which differs from the Feigenbaum diagram. Based on the formula of the passionary oscillator, a continuum cellular automaton has been developed, generating non-repeating symmetroids and quasi-chaotic distinctive structures. The system of passionary oscillators is considered as a possible basis for subsequent modeling of sociodynami

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CHENG, YUANJI, and LINA WANG. "REMARKS ON BIFURCATION IN ELLIPTIC BOUNDARY VALUE PROBLEMS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0178.

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Hetzler, Hartmut. "Bifurcation Analysis for Brake Squeal." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24814.

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This article presents a perturbation approach for the bifurcation analysis of MDoF vibration systems with gyroscopic and circulatory contributions, as they naturally arise from problems involving moving continua and sliding friction. Based on modal data of the underlying linear system, a multiple scales technique is utilized in order to find equations for the nonlinear amplitudes of the critical mode. The presented method is suited for an algorithmic implementation using commercial software and does not involve costly time-integration. As an engineering example, the bifurcation behaviour of a

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Mohammadi, Aliakbar. "Detection of hopf bifurcation using eigenvalue identification." In 2012 IV International Conference "Problems of Cybernetics and Informatics" (PCI). IEEE, 2012. http://dx.doi.org/10.1109/icpci.2012.6486386.

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Rezgui, Djamel, Mark Lowenberg, Mark Jones, and Claudio Monteggia. "Towards Industrialisation of Bifurcation Analysis in Rotorcraft Aeroelastic Problems." In AIAA Atmospheric Flight Mechanics Conference. American Institute of Aeronautics and Astronautics, 2012. http://dx.doi.org/10.2514/6.2012-4732.

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García-Huidobro, M., R. Manásevich, and J. R. Ward. "Bifurcation through higher order terms for problems at resonance." In The First 60 Years of Nonlinear Analysis of Jean Mawhin. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702906_0007.

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Reports on the topic "Bifurcation problems"

1

Mittelmann, Hans D. Continuation and Multi-Grid for Bifurcation Problems. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada274965.

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Mittelmann, Hans D. Continuation and Multi-Grid Methods for Bifurcation Problems. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada218904.

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Hong, Bin. Computational Methods for Bifurcation Problems with Symmetries on the Manifold. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada237146.

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Chan, Tony F. Numerical Methods for Solving Large Sparse Eigenvalue Problems and for the Analysis of Bifurcation Phenomena. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada244273.

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Chan, Tony F. Numerical Methods for Solving Large Sparse Eigenvalue Problems and for the Analysis of Bifurcation Phenomena. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada246470.

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