Results 21 to 30 of about 1,883 (165)
On Uniqueness of Limit Cycles in General Bogdanov–Takens Bifurcation [PDF]
International Journal of Bifurcation and Chaos, 2018 In this paper, we present a complete study of the well-known Bogdanov–Takens bifurcation and give a rigorous proof for the uniqueness of limit cycles.
Han, Maoan, Llibre, Jaume, Yang, Junmin
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Bogdanov–Takens Bifurcation of Codimension 3 in the Gierer–Meinhardt Model
International Journal of Bifurcation and Chaos, 2023 Bifurcation of the local Gierer–Meinhardt model is analyzed in this paper. It is found that the degenerate Bogdanov–Takens bifurcation of codimension 3 exists in the model, except for the saddle-node bifurcation and the Hopf bifurcation. That was not reported in the literature about this model.
Ranchao Wu, Lingling Yang
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Bogdanov-Takens bifurcation in predator-prey systems
Discrete & Continuous Dynamical Systems - S, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zeng, Bing, Deng, Shengfu, Yu, Pei
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Chaos in the Takens-Bogdanov bifurcation with O(2) symmetry [PDF]
, 2016 The Takens–Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation invariant in one spatial dimension with no left-right preference
A. M. Rucklidge +8 more
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Slow–fast Bogdanov–Takens bifurcations
Journal of Differential Equations, 2011 The paper deals with smooth families of slow-fast systems that represent a very general class of singular perturbation problems near a turning point. The authors introduce the notion of slow-fast Bogdanov-Takens bifurcation and provide a complete study of the perturbations from planar vector fields having a line of zeros, representing the singular ...
De Maesschalck, P., Dumortier, F.
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Takens-Bogdanov bifurcation of travelling wave solutions in pipe flow [PDF]
, 2010 The appearance of travelling-wave-type solutions in pipe Poiseuille flow that are disconnected from the basic parabolic profile is numerically studied in detail.
B. ECKHARDT +6 more
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Global bifurcations in the Takens-Bogdanov normal form with D_4 symmetry near the O(2) limit [PDF]
, 2001 The dynamics of the normal form of the Takens-Bogdanov bifurcation with D_4 symmetry is governed by a one-dimensional map near the gluing bifurcation and near the O(2) integrable limit, rather than the three-dimensional map one would expect.
Rucklidge, A.M.
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Complex Behaviors of Epidemic Model with Nonlinear Rewiring Rate
Complexity, 2020 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 ...
Ding Fang, Yongxin Zhang, Wendi Wang
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Dynamic analysis of a Leslie-Gower predator-prey model with the fear effect and nonlinear harvesting
Mathematical Biosciences and Engineering, 2023 In this paper, we investigate the stability and bifurcation of a Leslie-Gower predator-prey model with a fear effect and nonlinear harvesting. We discuss the existence and stability of equilibria, and show that the unique equilibrium is a cusp of ...
Hongqiuxue Wu, Zhong Li, Mengxin He
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Some results on homoclinic and heteroclinic connections in planar systems [PDF]
, 2009 Consider a family of planar systems depending on two parameters $(n,b)$ and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when $\Phi(n,b)=0.$ We present a method that allows to ...
Andronov A A +12 more
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