$QS205_{1}^{(8)}$

Description

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

Phase Portrait

Topological Invariants

TCSP
$205$

The quadratic differential system

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

with parameters: $b = 1$

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

With name $14$ in {J. C. Artés, J. Llibre and N. Vulpe}, Quadratic systems with a rational first integral of degree 2: A complete classification in the coefficient space $ R^{12$}, emph{Rend. Circ. Mat. Palermo}, textbf{56}, no. 3 (2007), 417--444.Note (for name $14$): missed orbit
With name $PL1$ in {L. Cairó and J. Llibre}, Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2. Nonlinear Anal. 67 (2007), no. 2, 327–348.
With name $Ric. D23$ 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 $QS205_{1}^{(8)}$ 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 $15$ in {J. C. Artés and J. Llibre}, Quadratic Hamiltonian vector fields, emph{J. Differential Equations}, { bf 107} (1994), 80--95.

Through the border $QS206_{1}^{(9)}$, by means of a bifurcation of type $deg$, we reach the neighbor $QS12_{1}^{(0)}$.

Bifurcation interface between the portrait $QS202_{1}^{(7)}$ and $QS202_{1}^{(7)}$.
Bifurcation interface between the portrait $QS204_{1}^{(7)}$ and $QS204_{1}^{(7)}$.