$QS75_{5}^{(2)}$

Description

Topological configuration of singularities: $s,a,a;(1,1)SN,(0,2)SN$

Phase Portrait

Topological Invariants

TCSP	Fin Sep	Inf Sep
$75$	$422$	$2211$

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 $U^2_{BC,08}$ in {J. C. Artés}, Systems of class BC2, {Preprint} (2026).
With name $5S18$ 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 $an01 Fig 2.33$ and $bn08 Fig 2.41$ in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
With names $an05 Fig. 5$ and $bn08 Fig. 13$ 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?).

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 $QS75_{5}^{(2)}$ could potentially exhibit an additional limit cycle bifurcating from the focus.