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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Displaying similar documents to “Simple examples of one-parameter planar bifurcations.”
Canard cycles and homoclinic bifurcation in a 3 parameter family of vector fields on the plane.
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.
Global qualitative investigation, limit cycle bifurcations and Applications of Polynomial Dynamical Systems
Gaiko, Valery
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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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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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Branching of periodic orbits from Kukles isochrones.
Toni, B. (1998)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Hoptf bifurcation from infinity for planar control systems.
Jaume Llibre, Enrique Ponce (1997)
Publicacions Matemàtiques
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Symmetric piecewise linear bi-dimensional systems are very common in control engineering. They constitute a class of non-differentiable vector fields for which classical Hopf bifurcation theorems are not applicable. For such systems, sufficient and necessary conditions for bifurcation of a limit cycle from the periodic orbit at infinity are given.
Bifurcation of closed orbits from a limit cycle in
Vinicio Moauro (1981)
Rendiconti del Seminario Matematico della Università di Padova
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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...