Global qualitative investigation, limit cycle bifurcations and Applications of Polynomial Dynamical Systems
Gaiko, Valery
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Displaying similar documents to “An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system”
Global qualitative investigation, limit cycle bifurcations and Applications of Polynomial Dynamical Systems
Cubic and quartic planar differential systems with exact algebraic limit cycles.
Bendjeddou, Ahmed, Cheurfa, Rachid (2011)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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A survey on homoclinic and heterocolinic orbits.
Feng, Beiye, Hu, Rui (2003)
Applied Mathematics E-Notes [electronic only]
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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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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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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.
Uniqueness of limit cycles bounded by two invariant parabolas
Eduardo Sáez, Iván Szántó (2012)
Applications of Mathematics
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In this paper we consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas.