Study of a very rich trhee parametric family of quadratic systems [ Back ]

15:30 to 16:30
UAB - Dept. Matemàtiques (C1/-128)
Joan Carles Artés


With the goal in mind of studying even larger families of quadratic systems which may help to close up to the complete class of phase portraits, and specially of the unstructurally stable systems of codimension 1, I proposed Alex Carlucci from Brasil, for his Ph. D. to study the family of systems with one finite saddle-node and one infinite saddle-node formed by the collision of two infinite singular points. The study has resulted in the family having 417 different phase portraits, 54 of them with limit cycles and more than 1/3 (concretelly 149) of them having different kinds of graphics. Moreover, there are two regions with 2 limit cycles and close to one of them, a continuous transition from a Hopf bifurcation to a loop formed by a weak saddle can be observed. The study of the bifurcations has been possible thanks to the use of algebraic invariants. As expected, this family has produced many of the missed phase portraits of codimension 1 that remained missed in a long term project that Jaume and me are developing.