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Explicit transversality conditions and local bifurcation diagrams for Bogdanov–Takens bifurcation on center manifolds

Physica D: Nonlinear Phenomena, 2019
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Yang Li, Kazuyuki Aihara, Hiroshi Kokubu
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Hopf and Bogdanov–Takens Bifurcations of a Delayed Bazykin Model

Qualitative Theory of Dynamical Systems
In this paper, the authors investigated the Hopf and Bogdanov-Takens bifurcations of a delayed Bazykin predator-prey model with predator intraspecific interactions and ratio-dependent functional response. And they established sufficient conditions for the existence of Hopf bifurcation.
Dongpo Hu, Zhaowen Zheng
exaly   +2 more sources

Bogdanov–Takens Bifurcation of a Class of Delayed Reaction–Diffusion System

International Journal of Bifurcation and Chaos, 2015
In this paper, a class of reaction–diffusion system with Neumann boundary condition is considered. By analyzing the generalized eigenvector associated with zero eigenvalue, an equivalent condition for the determination of Bogdonov–Takens (B–T) singularity is obtained.
Jianzhi Cao, Peiguang Wang, Rong Yuan, Yingying Mei   +3 more
openaire   +3 more sources

Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms

Ergodic Theory and Dynamical Systems, 1996
AbstractWe study a generic, real analytic unfolding of a planar diffeomorphism having a fixed point with unipotent linear part. In the analogue for vector fields an open parameter domain is known to exist, with a unique limit cycle. This domain is bounded by curves corresponding to a Hopf bifurcation and to a homoclinic connection.
Broer, H., Roussarie, R., Simó, C.
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Bogdanov–Takens bifurcation in an oscillator with positive damping and multiple delays

Nonlinear Dynamics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Jinling, Liu, Xia, Liang, Jinling
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Study of a degenerate bogdanov-takens bifurcation in a family of mechanical oscillators

Mechanics Research Communications, 1998
The authors study nonlinear second-order ordinary differential equations as models of generalized oscillators, and detect periodic behaviour by analysing the bifurcations in these oscillators. The most degenerate equilibria are considered, and a useful information is given about nontrivial oscillatory behaviours and their transitions. In particular, it
Freire, E., Gamero, E., Rondríguez-Luis, A. J.   +2 more
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DETECTING BOGDANOV–TAKENS BIFURCATION OF TRAVELING WAVES IN REACTION–DIFFUSION SYSTEMS

International Journal of Bifurcation and Chaos, 2006
In this paper we investigate the onset of instabilities in a model describing the propagation of the steady planar premixed combustion wave. In particular, we are interested in determining the Bogdanov–Takens bifurcation condition, which is investigated semi-analytically.
V. V. Gubernov, Harvinder S. Sidhu, Geoff N. Mercer   +2 more
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Bogdanov-Takens Bifurcation

2014
In the parameter space, curves of (classical) Poincare–Andronov–Hopf bifurcations, saddle-node bifurcations and homoclinic orbits emerge.In this chapter, we discuss the intricate patterns of heteroclinic orbits which appear near the corresponding bifurcation without parameters.
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A Note on the Bogdanov–Takens Bifurcation in the Romer Model with Learning by Doing

International Journal of Bifurcation and Chaos, 2017
This paper is aimed at describing the whole set of necessary and sufficient conditions for the emergence of multiple equilibria and global indeterminacy in the standard endogenous growth framework with learning by doing. The novelty of this paper relies on the application of the original Bogdanov–Takens bifurcation theorem, which allows us to ...
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Hopf and Bogdanov–Takens bifurcations in a coupled FitzHugh–Nagumo neural system with delay

Nonlinear Dynamics, 2010
A FitzHugh-Nagumo coupled neural systems with time delay are studied. The authors first prove Hopf bifurcation for this system. Spatio-temporal patterns of periodic solutions are obtained. Then Bogdanov-Takens bifurcation and complete bifurcation diagrams and phase portraits are presented. Examples illustrate the obtained theoretical results.
Weihua Jiang
exaly   +3 more sources