$QS204_{1}^{(7)}$

Description

Topological configuration of singularities: $∅,[ U, ∅ ];∅,[ U, N ]$

Phase Portrait

Topological Invariants

TCSP
$204$

The quadratic differential system

\[\begin{cases} \dot{x} = 0 \\ \dot{y} = 1 - x^{2} + f \, y \end{cases}\]

with parameters: $f = 1$

has the following phase portrait done with P4. If you want, you may download the P4 file here.

With name $d$ in {J. Llibre and M. F. da Silva}, Phase portraits of integrable quadratic systems with an invariant parabola and an invariant straight line, C. R. Math. Acad. Sci. Paris { bf 357} (2019), no.~2, 143--166; MR3927021
With name $Ric. D21$ in {J. C. Artés, J. Llibre, D. Schlomiuk and N. Vulpe}, Global analysis of Riccati quadratic differential systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 34} (2024), no.~1, Paper No. 2450004, 46 pp.; MR4701478
With name $QS204_{1}^{(7)}$ in {J. C. Artés and N. Vulpe}, The codimension of the phase portraits for degenerate quadratic differential systems, Bul. Acad. c Stiin c te Repub. Mold. Mat. { bf 2024}, no.~3(106), 29--53; MR4967334
With name $P29$ in {J. C. Artés, M. C. Mota and A. C. Rezende}, Quadratic differential systems with a finite saddle-node and an infinite saddle-node $(1, 1)SN$ - $({ rm B)$}, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 31} (2021), no.~9, Paper No. 2130026, 110 pp.; MR4291723

Through the border $QS205_{1}^{(8)}$, by means of a bifurcation of type $deg$, we reach the neighbor $QS204_{1}^{(7)}$.