Results 131 to 140 of about 332 (160)
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Bogdanov–Takens Bifurcation of a Class of Delayed Reaction–Diffusion System
International Journal of Bifurcation and Chaos, 2015In 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 +3 more
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Invariant circles in the Bogdanov-Takens bifurcation for diffeomorphisms
Ergodic Theory and Dynamical Systems, 1996AbstractWe 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, 2016zbMATH 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, 1998The 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. +2 more
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DETECTING BOGDANOV–TAKENS BIFURCATION OF TRAVELING WAVES IN REACTION–DIFFUSION SYSTEMS
International Journal of Bifurcation and Chaos, 2006In 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 +2 more
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Hopf and Bogdanov–Takens Bifurcations of a Delayed Bazykin Model
Qualitative Theory of Dynamical SystemsIn 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.
Liu, Ming +3 more
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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, 2017This 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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Stabilization and positioning control of a rolling disk by using the Bogdanov–Takens bifurcation
Physica D: Nonlinear Phenomena, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manuel Perez Molina
exaly +3 more sources
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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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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Limit cycles and homoclinic orbits and their bifurcation of Bogdanov-Takens system
Applied Mathematics and Mechanics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Cheng-biao, Liu, Jia
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