$QS75_{3}^{(2)}$

Description

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

Phase Portrait

Topological Invariants

TCSP	Fin Sep	Inf Sep
$75$	$431$	$3111$

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 $U^2_{BC,06}$ in {J. C. Artés}, Systems of class BC2, {Preprint} (2026).
With name $5S01$ 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 $bn01 Fig 2.34$, $fn01 Fig 2.36$, $an18 Fig 2.40$ and $fn06 Fig 2.42$ in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
With names $an03 Fig. 5$, $bn01 Fig. 6$, $fn01 Fig. 8$, $an10 Fig. 12$, $fn06 Fig. 14$ and $gn07 Fig. 14$ 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?).
With name $1.5L3$ in {J. C. Artés, J. Llibre and D. Schlomiuk}, The geometry of quadratic polynomial differential systems with a weak focus and an invariant straight line, emph{ Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{20}, no. 11 (2010), 3627--3662.

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 $QS75_{3}^{(2)}$ could potentially exhibit an additional limit cycle bifurcating from the focus.