$QS195_{1}^{(7)}$

Description

Topological configuration of singularities: $∅,[ | , ∅ ];N,[ | , (1,1) SN2 ]$

Phase Portrait

Topological Invariants

TCSP
$195$

The quadratic differential system

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

with parameters: $b = 0, \quad e = 1$

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

With name $Fig 1 B2-1.8L1$ in {J. C. Artés, L. Cairó and J. Llibre}, New Exploration of Phase portraits Classification of QuadraticPolynomial Differential Systems based on Invariant Theory. Applied Math. No. 1(0), (2025), 24pp.
With name $DP1$ in {J. C. Artés, L. Cairó and J. Llibre}, Phase portraits of the family IV of the quadratic polynomial differential systems, Qual. Theory Dyn. Syst. { bf 24} (2025), no.~2, Paper No. 66, 34 pp.; MR4860323
With name $Ric. D16$ 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 $QS195_{1}^{(7)}$ 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 $4.5.8L1$ in {J. C. Artés, M. C. Mota and A. C. Rezende}, Quadratic differential systems with a finite saddle-node and an infinite saddle-node $(1,1)SN$-$( roman{A)$}, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 31} (2021), no.~2, Paper No. 2150026, 24 pp.; MR4221748

{J. Llibre and X. Zhang}, Topological phase portraits of planar semi-linear quadratic vector fields, Houston J. Math. { bf 27} (2001), no.~2, 247--296; MR1874098

Through the border $QS196_{1}^{(8)}$, by means of a bifurcation of type $deg$, we reach the neighbor $QS195_{1}^{(7)}$.