$QS74_{13}^{(1)}$

Description

Topological configuration of singularities: $s,a,a;(1,1)SN,S,N$

Phase Portrait

Topological Invariants

TCSP	Fin Sep	Inf Sep
$74$	$422$	$211110$

The quadratic differential system

\[\begin{cases} \dot{x} = x+a \, y+e \, y^{2}+d \, (m \, x+g \, y+x \, y) \\ \dot{y} = m \, x+g \, y+x \, y \end{cases}\]

with parameters: $a = 1.9, \quad e = -1, \quad d = -3, \quad m = 1, \quad g = 1$

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

With name $Fig. 10$ in {J. Llibre and C. Pantazi}, Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023), no. 1, Paper No. 2350003, 54 pp.
With name $U^1_{C30}$ in {J. C. Artés, J. Llibre and A. C. Rezende}, Structurally unstable quadratic vector fields of codimension one, Birkhäuser/Springer, Cham, 2018, vi+267 pp.
With name $bn15 Fig 2.45$ in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
With name $bn15 Fig. 16$ in {J. W. Reyn and X. H. Huang}, Separatrix configurations of quadratic systems with finite multiplicity three and a $M^0_{1,1$ type of critical point at infinity}, Report U. Delft (1997?).

Bifurcation interface between the codimension 0 portrait $QS10_{14}^{(0)}$ and $QS5_{6}^{(0)}$.