\(QS86_{3}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(86\) | \(2\) | \(1111\) |
Example
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.
The phase portrait appears in the following papers
- With name \(U^2_{BC,03}\) in {J. C. Artés}, Systems of class BC2, {Preprint} (2026).
- With name \(5S02\) 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 \(Fig1b (2)\) in {J. W. Reyn}, Phase portraits of quadratic systems with finite multiplicity one, Nonlinear Anal. { bf 28} (1997), no.~4, 755--778; MR1420390
- With names \(hn01 Fig 2.38\), \(in01 Fig 2.39\), \(hn05 Fig 2.42\) and \(in06 Fig 2.42\) in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
- With names \(E50=e2\) and \(e10\) in {B. Coll, A. Gasull and J. Llibre}, Quadratic systems with a unique finite rest point, emph{Publ. Mat.}, textbf{32} (1988), 199--259.Note (for name \(e10\)): The system has 1 limit cycle.
- With names \(hn01 Fig. 10\), \(in01 Fig. 11\), \(hn05 Fig. 14\) and \(in06 Fig. 14\) 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?).Note (for name \(hn05 Fig. 14\)): one extra separatrixNote (for name \(in06 Fig. 14\)): one extra separatrix
- With name \(1.5L1\) in {J. C. Artés, A. C. Rezende and R. Oliveira}, Global phase portraits of quadratic polynomial differential systems with a semi-elemental triple node, emph{Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, { bf 23}, no. 8 (2013), 1350140, 21 pp.
- With name \(1.2L5\) 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 \(1.2L5\)): this portrait appears here with triple node, then no LC
Comments
Reyn did not find it in Reyn mf0, but maybe, LC is only possible with complex singularities
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 \(QS86_{3}^{(2)}\) could potentially exhibit an additional limit cycle bifurcating from the focus.