\(QS194_{1}^{(7)}\)

Description

Topological configuration of singularities: \(∅,[ ||, ∅ ];N,[ ||, ∅ ]\)

Phase Portrait

Topological Invariants

TCSP
\(194\)

The quadratic differential system

\[\begin{cases} \dot{x} = a + x^{2} \\ \dot{y} = 0 \end{cases}\]

with parameters: \(a = -1\)

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

With name \(C39\) in {C. A. Buzzi and D. J. Tonon}, Quadratic planar systems with two parallel invariant straight lines, Qual. Theory Dyn. Syst. { bf 7} (2009), no.~2, 295--316; MR2486677
With name \(LV_d.11\) in {D. Schlomiuk and N. Vulpe}, Global classification of the planar Lotka--Volterra differential systems according to their configurations of invariant straight lines, emph{J. Fixed Point Theory Appl.}, { bf 8}, no. 1 (2010), 177--245.
With name \(Ric. D17\) 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 \(QS194_{1}^{(7)}\) 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

Through the border \(QS196_{1}^{(8)}\), by means of a bifurcation of type \(deg\), we reach the neighbor \(QS137_{1}^{(3)}\).