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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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.