A survey on homoclinic and heterocolinic orbits.
Feng, Beiye, Hu, Rui (2003)
Applied Mathematics E-Notes [electronic only]
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Displaying similar documents to “Global qualitative investigation, limit cycle bifurcations and Applications of Polynomial Dynamical Systems”
A survey on homoclinic and heterocolinic orbits.
Simple examples of one-parameter planar bifurcations.
Armengol Gasull, Rafel Prohens (2000)
Extracta Mathematicae
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In this paper we give simple and low degree examples of one-parameter polynomial families of planar differential equations which present generic, codimension one, isolated, compact bifurcations. In contrast with some examples which appear in the usual text books each bifurcation occurs when the bifurcation parameter is zero. We study the total number of limit cycles that the examples present and we also make their phase portraits on the Poincaré sphere.
Bifurcation analysis of the Hénon map.
Zhusubaliyev, Zhanybai T., Rudakov, Vadim N., Soukhoterin, Evgeniy A., Mosekilde, Erik (2000)
Discrete Dynamics in Nature and Society
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Hopf-like bifurcations in planar piecewise linear systems.
Emilio Freire, Enrique Ponce, Francisco Torres (1997)
Publicacions Matemàtiques
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Continuous planar piecewise linear systems with two linear zones are considered. Due to their low differentiability specific techniques of analysis must be developed. Several bifurcations giving rise to limit cycles are pointed out.
Qualitative analysis for a class of plane systems.
Liu, Zhi-cong, Feng, Bei-ye (2004)
Applied Mathematics E-Notes [electronic only]
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Dynamical analysis of a demand governed market.
Barbiroli, Giancarlo, Palestini, Arsen, Ritelli, Daniele (2007)
APPS. Applied Sciences
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Canard cycles and homoclinic bifurcation in a 3 parameter family of vector fields on the plane.
Paulo Ricardo Da Silva (1999)
Publicacions Matemàtiques
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On the approximation of the limit cycles function.
Cherkas, L., Grin, A., Schneider, K.R. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system
Makoto Hayashi (2020)
Archivum Mathematicum
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In this paper, an improvement of the global region for the non-existence of limit cycles of the Bogdanov-Takens system, which is well-known in the Bifurcation Theory, is given by two ideas. The first is to apply the existence of the algebraic invariant curve of the system to the Bendixson-Dulac criterion, and the second is to consider a necessary condition in order that a closed orbit of the system includes two equilibrium points. In virtue of these methods, it shall be shown that our...