On a codimension 3 bifurcation of plane vector fields with symmetry
Milan Medveď (1990)
Czechoslovak Mathematical Journal
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Milan Medveď (1990)
Czechoslovak Mathematical Journal
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Borisovich, A.Y., Marzantowicz, W. (1996)
Abstract and Applied Analysis
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Milan Medveď (1985)
Czechoslovak Mathematical Journal
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Guckenheimer, John (1995)
Experimental Mathematics
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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.
Acosta, Antonio, Lizana, Marcos (2005)
Divulgaciones Matemáticas
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Laura Gardini, Iryna Sushko (2012)
ESAIM: Proceedings
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The object of the present paper is to give a qualitative description of the bifurcation mechanisms associated with a closed invariant curve in three-dimensional maps, leading to its doubling, not related to a standard doubling of tori. We propose an explanation on how a closed invariant attracting curve, born via Neimark-Sacker bifurcation, can be transformed into a repelling one giving birth to a new attracting closed invariant curve ...