$QS191_{1}^{(6)}$

Description

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

Phase Portrait

Topological Invariants

TCSP
$191$

The quadratic differential system

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

with parameters: $b = 0, \quad f = 1, \quad m = 1$

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

With name $Chap 2 7$ in {B. Imane and B. Souad}, Global phase portraits of quadratic differential systems exhibiting an invariant algebraic curve or an algebraic cubic first integral, {Ph.D. Universite Mohamed el Bachir}, (2020).
With name $c$ 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 $Ric. D14$ 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 $QS191_{1}^{(6)}$ 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 $P64$ in {J. C. Artés, A. C. Rezende and R. D. S. Oliveira}, The geometry of quadratic polynomial differential systems with a finite and an infinite saddle-node (C), emph{Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{25}, no. 3 (2015), 1530009, 111 pp.
With name $9.9L1$ 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