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.
@article{urn:eudml:doc:38627,
title = {Simple examples of one-parameter planar bifurcations.},
journal = {Extracta Mathematicae},
volume = {15},
year = {2000},
pages = {219-229},
zbl = {0986.34034},
mrnumber = {MR1792991},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38627}
}
Gasull, Armengol; Prohens, Rafel. Simple examples of one-parameter planar bifurcations.. Extracta Mathematicae, Tome 15 (2000) pp. 219-229. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38627/