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Relevant bibliographies by topics / Stability bifurcation

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Academic literature on the topic 'Stability bifurcation'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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Journal articles on the topic "Stability bifurcation"

1

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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2

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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3

Zhai, Yanhui, Ying Xiong, Xiaona Ma, and Haiyun Bai. "Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/242410.

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The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more,

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4

Jiang, Jiao, and Yongli Song. "Bifurcation Analysis and Spatiotemporal Patterns of Nonlinear Oscillations in a Ring Lattice of Identical Neurons with Delayed Coupling." Abstract and Applied Analysis 2014 (2014): 1–18. http://dx.doi.org/10.1155/2014/368652.

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We investigate the dynamics of a delayed neural network model consisting ofnidentical neurons. We first analyze stability of the zero solution and then study the effect of time delay on the dynamics of the system. We also investigate the steady state bifurcations and their stability. The direction and stability of the Hopf bifurcation and the pitchfork bifurcation are analyzed by using the derived normal forms on center manifolds. Then, the spatiotemporal patterns of bifurcating periodic solutions are investigated by using the symmetric bifurcation theory, Lie group theory andS1-equivariant de

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5

Xu, Changjin, and Xiaofei He. "Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms." Abstract and Applied Analysis 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/697630.

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A class of two-neuron networks with resonant bilinear terms is considered. The stability of the zero equilibrium and existence of Hopf bifurcation is studied. It is shown that the zero equilibrium is locally asymptotically stable when the time delay is small enough, while change of stability of the zero equilibrium will cause a bifurcating periodic solution as the time delay passes through a sequence of critical values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the n

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6

Liu, Yi Jing, Zhi Shu Li, Xiao Mei Cai, and Ya Lan Ye. "Local Stability and Hopf Bifurcation Analysis of the Arneodo’s System." Applied Mechanics and Materials 130-134 (October 2011): 2550–57. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2550.

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The chaotic behaviors of the Arneodo’s system are investigated in this paper. Based on the Arneodo's system characteristic equation, the equilibria of the system and the conditions of Hopf bifurcations are obtained, which shows that Hopf bifurcations occur in this system. Then using the normal form theory, we give the explicit formulas which determine the stability of bifurcating periodic solutions and the direction of the Hopf bifurcation. Finally, some numerical examples are employed to demonstrate the effectiveness of the theoretical analysis.

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Liu, Ping, Junping Shi, Rui Wang, and Yuwen Wang. "Bifurcation Analysis of a Generic Reaction–Diffusion Turing Model." International Journal of Bifurcation and Chaos 24, no. 04 (2014): 1450042. http://dx.doi.org/10.1142/s0218127414500424.

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A generic Turing type reaction–diffusion system derived from the Taylor expansion near a constant equilibrium is analyzed. The existence of Hopf bifurcations and steady state bifurcations is obtained. The bifurcation direction and the stability of the bifurcating periodic obits are calculated. Numerical simulations are included to show the rich spatiotemporal dynamics.

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8

Aizawa, H., K. Ikeda, M. Osawa, and J. M. Gaspar. "Breaking and Sustaining Bifurcations in SN-Invariant Equidistant Economy." International Journal of Bifurcation and Chaos 30, no. 16 (2020): 2050240. http://dx.doi.org/10.1142/s0218127420502405.

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This paper elucidates the bifurcation mechanism of an equidistant economy in spatial economics. To this end, we derive the rules of secondary and further bifurcations as a major theoretical contribution of this paper. Then we combine them with pre-existing results of direct bifurcation of the symmetric group [Formula: see text] [Elmhirst, 2004]. Particular attention is devoted to the existence of invariant solutions which retain their spatial distributions when the value of the bifurcation parameter changes. Invariant patterns of an equidistant economy under the replicator dynamics are obtaine

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WANG, HUAILEI, and HAIYAN HU. "BIFURCATION ANALYSIS OF A DELAYED DYNAMIC SYSTEM VIA METHOD OF MULTIPLE SCALES AND SHOOTING TECHNIQUE." International Journal of Bifurcation and Chaos 15, no. 02 (2005): 425–50. http://dx.doi.org/10.1142/s0218127405012326.

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This paper presents a detailed study on the bifurcation of a controlled Duffing oscillator with a time delay involved in the feedback loop. The first objective is to determine the bifurcating periodic motions and to obtain the global diagrams of local bifurcations of periodic motions with respect to time delay. In order to determine the bifurcation point, an analysis on the stability switches of the trivial equilibrium is first performed for all possible parametric combinations. Then, by means of the method of multiple scales, an analysis on the local bifurcation of periodic motions is given.

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Xu, Changjin, and Peiluan Li. "Dynamical Analysis in a Delayed Predator-Prey Model with Two Delays." Discrete Dynamics in Nature and Society 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/652947.

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A class of Beddington-DeAngelis functional response predator-prey model is considered. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are given.

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Dissertations / Theses on the topic "Stability bifurcation"

1

Kwok, Loong-Piu. "Viscous cross-waves: Stability and bifurcation." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184441.

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In the first part of this thesis, the nonlinear Schrodinger equation for inviscid cross-waves near onset is found to be modified by viscous linear damping and detuning. The accompanying boundary condition at the wavemaker is also modified by damping from the wavemaker meniscus. The relative contributions of the free-surface, sidewalls, bottom, and wavemaker viscous boundary layers are computed. It is shown that viscous dissipation due to the wavemaker meniscus breaks the symmetry of the neutral curve. In the second part, existence and stability of steady solutions to the nonlinear Schrodinger

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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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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.

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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.

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Korobeinikov, Andrei. "Stability and bifurcation of deterministic infectious disease models." Thesis, University of Auckland, 2001. http://wwwlib.umi.com/dissertations/fullcit/3015611.

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Autonomous deterministic epidemiological models are known to be asymptotically stable. Asymptotic stability of these models contradicts observations. In this thesis we consider some factors which were suggested as able to destabilise the system. We consider discrete-time and continuous-time autonomous epidemiological models. We try to keep our models as simple as possible and investigate the impact of different factors on the system behaviour. Global methods of dynamical systems theory, especially the theory of bifurcations and the direct Lyapunov method are the main tools of our analysis.

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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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Raina, Gaurav. "Congestion control for the internet : stability and bifurcation analysis." Thesis, University of Cambridge, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613765.

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Xu, Yeyin. "STABILITY AND BIFURCATION DYNAMICS OF JOURNAL BEARING ROTOR SYSTEMS." OpenSIUC, 2020. https://opensiuc.lib.siu.edu/dissertations/1835.

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In this dissertation, the mechanical models of 2-DOF and 4-DOF nonlinear journal bearing rotor systems are established. A more accurate model of oil film forces is derived from Reynolds equations. The periodic motions in such nonlinear journal bearing systems are obtained through discrete mapping method. Such a semi-analytical method constructs an implicit discrete mapping structure for periodic motions by discretization of the continuous journal bearing rotor differential equations. Stable and unstable periodic solutions of periodic motions are obtained with prescribed accuracy. The bifurcati

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Hsia, Chun-Hsiung. "Bifurcation and stability in fluid dynamics and geophysical fluid dynamics." [Bloomington, Ind.] : Indiana University, 2006. 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:3223038.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2006.<br>"Title from dissertation home page (viewed June 28, 2007)." Source: Dissertation Abstracts International, Volume: 67-06, Section: B, page: 3165. Adviser: Shouhong Wang.

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Pearce, S. P. "Bifurcation and stability of elastic membranes : theory and biological applications." Thesis, Keele University, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.518311.

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Books on the topic "Stability bifurcation"

1

Seydel, R. Practical bifurcation and stability analysis. 3rd ed. Springer, 2010.

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2

D, Joseph Daniel, ed. Elementary stability and bifurcation theory. 2nd ed. Springer-Verlag, 1990.

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3

Troger, Hans, and Alois Steindl. Nonlinear Stability and Bifurcation Theory. Springer Vienna, 1991. http://dx.doi.org/10.1007/978-3-7091-9168-2.

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4

Seydel, Rüdiger. Practical Bifurcation and Stability Analysis. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-1740-9.

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5

Iooss, Gérard, and Daniel D. Joseph. Elementary Stability and Bifurcation Theory. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-0997-3.

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6

Nguyen, Q. S., ed. Bifurcation and Stability of Dissipative Systems. Springer Vienna, 1993. http://dx.doi.org/10.1007/978-3-7091-2712-4.

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7

Bigoni, Davide, and Oleg Kirillov, eds. Dynamic Stability and Bifurcation in Nonconservative Mechanics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-93722-9.

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8

Luo, Albert C. J. Bifurcation and Stability in Nonlinear Dynamical Systems. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22910-8.

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9

Luo, Albert C. J. Bifurcation and Stability in Nonlinear Discrete Systems. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5212-0.

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10

Seydel, R. Practical bifurcation and stability analysis: From equilibrium to chaos. 2nd ed. Springer-Verlag, 1994.

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Book chapters on the topic "Stability bifurcation"

1

Thomsen, Jon Juel. "Bifurcation Analysis." In Vibrations and Stability. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68045-9_5.

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2

Hale, Jack K., Luis T. Magalhães, and Waldyr M. Oliva. "Stability and Bifurcation." In Dynamics in Infinite Dimensions. Springer New York, 2002. http://dx.doi.org/10.1007/0-387-22896-9_5.

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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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4

Troger, Hans, and Alois Steindl. "Reduction process, bifurcation equations." In Nonlinear Stability and Bifurcation Theory. Springer Vienna, 1991. http://dx.doi.org/10.1007/978-3-7091-9168-2_3.

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5

Holmes, Mark H. "Introduction to Bifurcation and Stability." In Texts in Applied Mathematics. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-5477-9_6.

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6

Lakshmanan, M., and D. V. Senthilkumar. "Linear Stability and Bifurcation Analysis." In Dynamics of Nonlinear Time-Delay Systems. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14938-2_2.

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7

Lacarbonara, Walter. "Stability and Bifurcation of Structures." In Nonlinear Structural Mechanics. Springer US, 2012. http://dx.doi.org/10.1007/978-1-4419-1276-3_2.

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Holmes, Mark H. "Introduction to Bifurcation and Stability." In Texts in Applied Mathematics. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-5347-1_6.

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9

Pignataro, M. "Stability, Bifurcation and Postbuckling Analysis." In Coupled Instabilities in Metal Structures. Springer Vienna, 1998. http://dx.doi.org/10.1007/978-3-7091-2510-6_2.

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10

Banichuk, Nikolay, Alexander Barsuk, Juha Jeronen, Tero Tuovinen, and Pekka Neittaanmäki. "Bifurcation Analysis for Polynomial Equations." In Stability of Axially Moving Materials. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23803-2_2.

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Conference papers on the topic "Stability bifurcation"

1

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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2

Mureithi, N. W., and M. Rodriguez. "Stability and Bifurcation Analysis of a Forced Cylinder Wake." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79778.

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We present a study on the dynamics of a cylinder wake subjected to forced excitation. Williams et al. (1992) discovered that the spatial symmetry of the excitation plays a crucial role in determining the resulting wake dynamics. Reflection-symmetric forcing was found to affect the Karman wake much more strongly compared to Z2(κ, π) asymmetric forcing. For low forcing amplitudes, the existence of a nonlinear mode interaction mechanism was postulated to explain the observed “beating” phenomenon observed in the wake. Previous work by the authors (Mureithi et al. 2002, 2003) presented general form

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3

Shukla, A., and D. F. Thompson. "Bifurcation stability of servo-hydraulic systems." In Proceedings of American Control Conference. IEEE, 2001. http://dx.doi.org/10.1109/acc.2001.946274.

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You-jie, Ma, Wen Hu-long, Zhou Xue-song, Li Ji, and Yang Hai-shan. "Bifurcation Analysis on Power System Voltage Stability." In 2009 Second International Conference on Intelligent Computation Technology and Automation. IEEE, 2009. http://dx.doi.org/10.1109/icicta.2009.474.

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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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6

Gala´n-Vioque, J., M. A. Lago, and J. Valverde. "Stability and Bifurcations in a Model of a Follower Loaded Rod." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47441.

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We analyse a continuous Cosserat model of a visco-elastic rod subjected to a combination of a conservative load and a follower term in one of the ends. The formalism takes into account the geometric non linearities that appear for large deformations from the straight solution. The resulting equation is a PDE whose solution can be analysed for special cases and the eigenvalues of the linearisation can be computed by a combination of numerical continuation and bifurcation results. We illustrate this method analysing the bifurcations of the straight solution of a rod subjected to a follower force

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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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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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Kengne, J., J. C. Chedjou, K. Kyamakya, and I. Moussa. "Stability and bifurcation analysis in transformer coupled oscillators." In 2009 2nd International Workshop on Nonlinear Dynamics and Synchronization (INDS). IEEE, 2009. http://dx.doi.org/10.1109/inds.2009.5227974.

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Zhang, Yue, Kuanquan Wang, Yongfeng Yuan, Dong Sui, Henggui Zhang, and Henggui Zhang. "Stability and bifurcation analysis of Hodgkin-Huxley model." In 2013 IEEE International Conference on Bioinformatics and Biomedicine (BIBM). IEEE, 2013. http://dx.doi.org/10.1109/bibm.2013.6732717.

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Reports on the topic "Stability bifurcation"

1

Rosenblat, S. Bifurcation and Stability of Complex Flows. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada161405.

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2

Marsden, J. E., and T. S. Ratiu. Stability, bifurcation, and control of Hamiltonian systems. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10142335.

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Marsden, J. E., and T. S. Ratiu. Stability, bifurcation, and control of Hamiltonian systems. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/6642330.

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4

Kevrekidis, Ioannis G. Enabling-Dynamic Simulators: Stability, Bifurcation and Control Computations for Distributed Parameter Systems. Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada405411.

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Brush, L. N., R. F. Sekerka, and G. B. McFadden. A numerical and analytical study of nonlinear bifurcations associated with the morphological stability of two-dimensional single crystals. National Institute of Standards and Technology, 1989. http://dx.doi.org/10.6028/nist.ir.89-4193.

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