$QS30_{1}^{(2)}$

Description

Topological configuration of singularities: $a,a,sn;S$

Phase Portrait

Topological Invariants

TCSP	Fin Sep	Inf Sep
$30$	$420$	$11$

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 $U^2_AD,12$ in {J. C. Artés}, Structurally unstable quadratic vector fields of codimension two: families possessing one finite saddle-node and a separatrix connection, Qual. Theory Dyn. Syst. { bf 23} (2024), no.~1, Paper No. 40, 88 pp.; MR4662466
With name $7S17$ in {J. C. Artés and C. Trullàs}, Quadratic Differential Systems with a Weak Focus of First-Order and a Finite Saddle-Node, {International Journal of Bifurcation and Chaos, Vol. 36, No. 6 (2026) 2630013 (99 pages)}
With name $5.7L9$ in {J. C. Artés, A. C. Rezende and R. D. S. Oliveira}, The geometry of quadratic polynomial differential systems with a finite and an infinite saddle-node (C), emph{Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{25}, no. 3 (2015), 1530009, 111 pp.Note (for name $5.7L9$): wrong arrow inside graphic as detected in AD

If the stability of the focus inside the graphic is the opposite, we obtain portrait $QS030^2_1^C$ which is conjectured not to exist
This phase portrait appears in J. C. Artés and C. Trullàs ({International Journal of Bifurcation and Chaos, Vol. 36, No. 6 (2026) 2630013 (99 pages)}) featuring a weak focus of first order. Consequently, a configuration structurally equivalent to $QS30_{1}^{(2)}$ could potentially exhibit an additional limit cycle bifurcating from the focus.