We study phase portraits of quadratic systems with a unique finite singularity. We prove that there are 111 different phase portraits without limit cycles and that 13 of them are realizable with exactly one limit cycle. In order to finish completely our study two problems remain open: the realization of one topologically possible phase portrait, and to determine the exact number of limit cycles for a subclass of these systems.
@article{urn:eudml:doc:41057,
title = {Quadratic systems with a unique finite rest point.},
journal = {Publicacions Matem\`atiques},
volume = {32},
year = {1988},
pages = {199-259},
zbl = {0674.34027},
mrnumber = {MR0975899},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41057}
}
Coll, Bartomeu; Gasull, Armengol; Llibre, Jaume. Quadratic systems with a unique finite rest point.. Publicacions Matemàtiques, Tome 32 (1988) pp. 199-259. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41057/