$QS74_{2}^{(2)}$

Description

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

Phase Portrait

Topological Invariants

TCSP	Fin Sep	Inf Sep
$74$	$430$	$210110$

The quadratic differential system

\[\begin{cases} \dot{x} = P_x(x,y) \\ \dot{y} = P_y(x,y) \end{cases}\]

has the following phase portrait done with P4.

With name $CD11$ in {J. C. Artés}, Systems of class CD, {Preprint} (2026).
With name $7S10$ in {J. C. Artés and L. Cairó}, Phase portraits of quadratic differential systems with a weak focus and a (1,1) SN, {Preprint} (2026).
With names $bn10 Fig 2.45$, $fn08 Fig 2.47$ and $an41 Fig 2.51$ in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).Note (for name $bn10 Fig 2.45$): uncompleteNote (for name $fn08 Fig 2.47$): uncompleteNote (for name $an41 Fig 2.51$): uncomplete
With names $an16 Fig. 15$, $bn10 Fig. 16$, $fn08 Fig. 18$ and $an25 Fig. 22$ 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?).Note (for name $an16 Fig. 15$): uncomplete. I do not like the position of the loopNote (for name $bn10 Fig. 16$): uncompleteNote (for name $fn08 Fig. 18$): uncompleteNote (for name $an25 Fig. 22$): uncomplete

This phase portrait appears in J. C. Artés and L. Cairó ({Preprint} (2026)) featuring a weak focus of first order. Consequently, a configuration structurally equivalent to $QS74_{2}^{(2)}$ could potentially exhibit an additional limit cycle bifurcating from the focus.