$QS76_{2}^{(2)}$

Description

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

Phase Portrait

Topological Invariants

TCSP	Fin Sep	Inf Sep
$76$	$441$	$212110$

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 $CD28$ in {J. C. Artés}, Systems of class CD, {Preprint} (2026).
With name $7S13$ 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 $cp09 Fig 2.65$ in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
With name $cp09 Fig. 36$ 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 $QS76_{2}^{(2)}$ could potentially exhibit an additional limit cycle bifurcating from the focus.