$QS73_{2}^{(2)}$

Description

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

Phase Portrait

Topological Invariants

TCSP	Fin Sep	Inf Sep
$73$	$411$	$11$

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 $CD03$ in {J. C. Artés}, Systems of class CD, {Preprint} (2026).
With name $3$ in {A. Ferragut, J. D. García-Saldaña and C. Valls}, Phase portraits of Abel quadratic differential systems of second kind with symmetries, Dyn. Syst. { bf 34} (2019), no.~2, 301--333; MR3941199
With name $P05$ in {J. Llibre and C. Valls}, Global phase portraits for the Abel quadratic polynomial differential equations of second kind with $Z_2$-symmetries, Canad. Math. Bull. { bf 61} (2018), no.~1, 149--165; MR3746481
With name $4S13$ 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 name $bs07 Fig. 2,30$ in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
With name $bs07 Fig. 4$ 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 $1S1$ 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 $QS73_{2}^{(2)}$ could potentially exhibit an additional limit cycle bifurcating from the focus.