Relevant bibliographies by topics / Transcritical bifurcation

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

Academic literature on the topic 'Transcritical bifurcation'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Transcritical bifurcation"

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Virgin, L. N., and R. Wiebe. "On damping in the vicinity of critical points." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1993 (2013): 20120426. http://dx.doi.org/10.1098/rsta.2012.0426.

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The effect of damping on the behaviour of oscillations in the vicinity of bifurcations of nonlinear dynamical systems is investigated. Here, our primary focus is single degree-of-freedom conservative systems to which a small linear viscous energy dissipation has been added. Oscillators with saddle–node, pitchfork and transcritical bifurcations are shown analytically to exhibit several interesting characteristics in the free decay response near a bifurcation. A simple mechanical oscillator with a transcritical bifurcation is used to experimentally verify the analytical results. A transcritical
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Saputra, Kie Van Ivanky. "Dynamical Systems with a Codimension-One Invariant Manifold: The Unfoldings and Its Bifurcations." International Journal of Bifurcation and Chaos 25, no. 06 (2015): 1550091. http://dx.doi.org/10.1142/s0218127415500911.

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We investigate a dynamical system having a special structure namely a codimension-one invariant manifold that is preserved under the variation of parameters. We derive conditions such that bifurcations of codimension-one and of codimension-two occur in the system. The normal forms of these bifurcations are derived explicitly. Both local and global bifurcations are analyzed and yield the transcritical bifurcation as the codimension-one bifurcation while the saddle-node–transcritical interaction and the Hopf–transcritical interactions as the codimension-two bifurcations. The unfolding of this de
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Geng, Fengjie, and Junfang Zhao. "Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria." Scientific World Journal 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/585609.

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The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip and an inclination flip. When the nonhyperbolic equilibrium does not undergo a transcritical bifurcation, we establish the coexistence and noncoexistence of the periodic orbits and homoclinic orbits. While the nonhyperbolic equilibrium undergoes the transcritical bifurcation, we obtain the noncoexistence of the periodic orbits and homoclinic orb
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GENG, FENGJIE, DAN LIU, and DEMING ZHU. "BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION." International Journal of Bifurcation and Chaos 18, no. 04 (2008): 1069–83. http://dx.doi.org/10.1142/s0218127408020847.

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The bifurcations of generic heteroclinic loop with one nonhyperbolic equilibrium p1and one hyperbolic saddle p2are investigated, where p1is assumed to undergo transcritical bifurcation. Firstly, we discuss bifurcations of heteroclinic loop when transcritical bifurcation does not happen, the persistence of heteroclinic loop, the existence of homoclinic loop connecting p1(resp. p2) and the coexistence of one homoclinic loop and one periodic orbit are established. Secondly, we analyze bifurcations of heteroclinic loop accompanied by transcritical bifurcation, namely, nonhyperbolic equilibrium p1s
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Yabuno, Hiroshi, Masahiko Hasegawa, and Manami Ohkuma. "Bifurcation control for a parametrically excited cantilever beam by linear feedback." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 8 (2012): 1987–99. http://dx.doi.org/10.1177/0954406212442603.

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In this article, we propose a bifurcation control method for a parametrically excited cantilever beam by linear feedback. Quadratic damping plays a dominant role in the nonlinear response of the parametrically excited cantilever beam, and two transcritical bifurcations can exist in the frequency–response curve. In the relatively high-amplitude excitation or in sweeping the excitation amplitude, there are two saddle-node bifurcations in addition to the transcritical bifurcations. The discontinuous bifurcation as a saddle-node bifurcation induces jumping phenomena in the sweeps of the excitation
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Liu, Xingbo. "Homoclinic flip bifurcations accompanied by transcritical bifurcation." Chinese Annals of Mathematics, Series B 32, no. 6 (2011): 905–16. http://dx.doi.org/10.1007/s11401-011-0675-y.

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DU, DONGYUN, and YUN TANG. "BIFURCATION ANALYSIS OF DIFFERENTIAL-DIFFERENCE-ALGEBRAIC EQUATIONS." International Journal of Bifurcation and Chaos 14, no. 08 (2004): 2853–65. http://dx.doi.org/10.1142/s0218127404010886.

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The dynamics of differential-difference-algebraic equations is studied. The paper extends the study of the local bifurcations to transcritical and pitchfork bifurcation under certain nondegenerate conditions using Lyapunov–Schmidt reduction. Furthermore, an improved version of singularity induced bifurcation theorem is given in this paper.
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Fang, Ding, Yongxin Zhang, and Wendi Wang. "Complex Behaviors of Epidemic Model with Nonlinear Rewiring Rate." Complexity 2020 (May 8, 2020): 1–16. http://dx.doi.org/10.1155/2020/7310347.

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An SIS propagation model with the nonlinear rewiring rate on an adaptive network is considered. It is found by bifurcation analysis that the model has the complex behaviors which include the transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation. Especially, a bifurcation curve with “S” shape emerges due to the nonlinear rewiring rate, which leads to multiple equilibria and twice saddle-node bifurcations. Numerical simulations show that the model admits a homoclinic bifurcation and a saddle-node bifurcation of the limit cycle.
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YUAN, YUAN, and JUNJIE WEI. "MULTIPLE BIFURCATION ANALYSIS IN A NEURAL NETWORK MODEL WITH DELAYS." International Journal of Bifurcation and Chaos 16, no. 10 (2006): 2903–13. http://dx.doi.org/10.1142/s0218127406016537.

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A synchronized neural network model with delays is considered. The bifurcations arising from the zero root of the corresponding characteristic equation have been studied by employing the center manifold theorem, normal form method and bifurcation theory. It is shown that the system may exhibit transcritical/pitchfork bifurcation, or Bogdanov–Takens bifurcation. Some numerical simulation examples are given to justify the theoretical results.
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Ruan, Mianjian, Xianyi Li, and Bo Sun. "More complex dynamics in a discrete prey-predator model with the Allee effect in prey." Mathematical Biosciences and Engineering 20, no. 11 (2023): 19584–616. http://dx.doi.org/10.3934/mbe.2023868.

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<abstract><p>In this paper, we revisit a discrete prey-predator model with the Allee effect in prey to find its more complex dynamical properties. After pointing out and correcting those known errors for the local stability of the unique positive fixed point $ E_*, $ unlike previous studies in which the author only considered the codim 1 Neimark-Sacker bifurcation at the fixed point $ E_*, $ we focus on deriving many new bifurcation results, namely, the codim 1 transcritical bifurcation at the trivial fixed point $ E_1, $ the codim 1 transcritical and period-doubling bifurcations a
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Dissertations / Theses on the topic "Transcritical bifurcation"

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Lim, Tzong-Shin, and 林宗欣. "Study on the stochastic response around transcritical bifurcation and its experimental counterpart in semiconductor lasers." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/75752236864532984760.

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碩士<br>國立成功大學<br>物理學系<br>86<br>We explore the stochastic response around the transcritical bifurcationand its experinental counterpart in semiconductor lasers. Peterman had experimentallyshow that the relative intensity noise fluctuation around laser threshold (bifurcation) would be greatly enhanced on an analysis of the relative intensitynoise (RIN) in rf-spectrum domain (Opt. Quantum Electron. 12 (1980) 207-219). TheoreticalRIN exploration had also been illustrated in a multi-mode laser mo
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Book chapters on the topic "Transcritical bifurcation"

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Liebscher, Stefan. "Transcritical Bifurcation." In Bifurcation without Parameters. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10777-6_4.

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Liebscher, Stefan. "Degenerate Transcritical Bifurcation." In Bifurcation without Parameters. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10777-6_8.

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Ferrell, James E. "Transcritical Bifurcations in Phase Separation and Infectious Disease." In Systems Biology of Cell Signaling. Garland Science, 2021. http://dx.doi.org/10.1201/9781003124269-10.

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Sajan, Ankit Kumar, and Balram Dubey. "Stability Switching in a Cooperative Prey-Predator Model with Transcritical and Hopf-bifurcations." In Nonlinear Dynamics and Applications. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99792-2_84.

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Jiang, Zhen-Kun, Ming-Shan Li, Kai-Le Qiu, Guo-Qiang Qiang, Dong-Huan He, and Xiao-Liang Zhou. "Dynamic Analysis of Cournot-Bertrand Double Oligopoly Hybrid Competition Model." In Modern Management based on Big Data V. IOS Press, 2024. http://dx.doi.org/10.3233/faia240248.

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In this paper, we investigate the Cournot-Bertrand double oligopoly hybrid competition model proposed by Zhu et al. (2021). By using the central manifold reduction theorem we analyze the structural stability of the model for three fixed points. We show that a subcritical (supercritical) flip bifurcation occurs at first (second and third) fixed point. This reflects that in the market competition, there will be a 2-period cycle between two firms. When subcritical flip bifurcation occurs, the 2-period cycle is unstable and the objective function values of both firms gradually deviates from the cy
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Conference papers on the topic "Transcritical bifurcation"

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Muller, Matthias A., Steffen Waldherr, and Frank Allgower. "The transcritical bifurcation in absolutely stable feedback systems." In 2009 European Control Conference (ECC). IEEE, 2009. http://dx.doi.org/10.23919/ecc.2009.7074722.

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Yuan, Yuan Y. "Multiple Bifurcations of Synchronized Oscillators With Delays." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84584.

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The synchronized oscillator with two discrete time delays is considered. The local stability of the zero solution of this system is investigated by studying the distributions of the eigenvalues of the system. A complete bifurcation analysis is given by employing the center manifold theorem, normal form method and bifurcation theorem. It is shown that the trivial fixed point may lose stability via a transcritical/pitchfork bifurcation, Hopf bifurcation or Bogdanov-Takens bifurcation. Some numerical simulation examples are given for justify the theoretical results.
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MEIJER, H. G. E. "A TRANSCRITICAL-FLIP BIFURCATION IN A MODEL FOR A ROBOT-ARM." In Proceedings of the International Conference on SPT 2004. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702142_0025.

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Qian, Changzhao, Changping Chen, and Liming Dai. "Bifurcation Control for a S.D.O.F. Nonlinear System to a Principal Parametric Resonance With Time Delay." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-38122.

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The bifurcation and response of one-degree-of-freedom system with quadratic and cubic non-linearities to a principal parametric is investigated. Using time delay damp, the bifurcation is controlled. The method of multiple scales is used to determine the equations that describe to second order the modulation of the amplitude and phase with time about one of foci. These equations are used to determine the fixed points and their stability. Because there are some items which are time delay’s function in the bifurcation equations, changing the time delay parameters may change the bifurcation form o
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Huang, ZaiTang. "The fractional Lévy-driven a simple dynamics system: Transcritical bifurcation." In 2013 2nd International Symposium on Instrumentation & Measurement, Sensor Network and Automation (IMSNA). IEEE, 2013. http://dx.doi.org/10.1109/imsna.2013.6742805.

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Garg, Pardeep, Sriram Hebbalguppe Krishna, Pramod Kumar, Thomas Conboy, and Clifford Ho. "Advanced Low Pressure Cycle for Concentrated Solar Power Generation." In ASME 2014 8th International Conference on Energy Sustainability collocated with the ASME 2014 12th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/es2014-6545.

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Turbine inlet pressures of ∼ 300 bar in case of CO2 based cycles call for redesigning the cycle in such a way that the optimum high side pressures are restricted to the discharge pressure limits imposed by currently available commercial compressors (∼150 bar) for distributed power generation. This leads to a cycle which is a combination of a transcritical condensing and a subcritical cycle with an intercooler and a bifurcation system in it. Using a realistic thermodynamic model, it is predicted that the cycle with the working fluid as a non-flammable mixture of 48.5 % propane and rest CO2 deli
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Wang, Deshi, Renbin Xiao, and Ming Yang. "The Attitude Stability for Longitudinal Motion of Underwater Vehicle." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21607.

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Abstract Although the equations describing the longitudinal motions of underwater vehicles are typically nonlinear, the linearized equations are still employed to design the depth controller by the traditional analysis methods in engineering for the sake of simplicity. The reduction of the nonlinearity loses the dynamics near the singular points, which may be responsible for the sudden climb or dive. The nonlinear systems limited in the longitudinal plane of the underwater vehicles are analyzed on center manifold through the bifurcation theory. It focuses on the case that single zero root in J
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Perret-Liaudet, Joe¨l, and Emmanuel Rigaud. "Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84989.

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The purpose of this paper is to investigate experimental responses of a preloaded vibroimpact Hertzian contact to an order 2 superharmonic excitation. A test rig is used, corresponding to a double sphere-plane contact preloaded by the weight of a moving body. Typical response curves are obtained kinder the superharmonic excitation. The Hertzian non linearity constitutes the precursor of vibroimpacts established over a wide frequency range. This behaviour can be related to the existence of a transcritical bifurcation. In conjuction with the experiments, numerical results lead to the same conclu
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