\(QS132_{1}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(132\) | \(41\) | \(211111\) |
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 \(CC4\) in {J. C. Artés}, Systems of class CC, {Preprint} (2026).
- With names \(V13\) and \(V14\) in {J. C. Artés, Hebai Chen, L. M. Ferrer and Man Jia}, Quadratic vector fields in class $I$, Dyn. Syst. { bf 40} (2025), no.~2, 191--222; MR4906437Note (for name \(V13\)): The system has 1 limit cycle.
- With names \(AV18\) and \(AV19\) in {J. C. Artés, L. Cairó and J. Llibre}, Phase portraits of the family IV of the quadratic polynomial differential systems, Qual. Theory Dyn. Syst. { bf 24} (2025), no.~2, Paper No. 66, 34 pp.; MR4860323Note (for name \(AV19\)): The system has 1 limit cycle.
- With name \(18\) in {A. Ferragut and C. Valls}, Phase portraits of Abel quadratic differential systems of the second kind, Dyn. Syst. { bf 33} (2018), no.~4, 581--601; MR3869849
- With names \(25\) and \(28\) in {J. Llibre and X. Zhang}, Topological phase portraits of planar semi-linear quadratic vector fields, Houston J. Math. { bf 27} (2001), no.~2, 247--296; MR1874098Note (for name \(28\)): The system has 1 limit cycle.
- With names \(Fig 2 c\) and \(Fig 2 h\) in {M. Jia, H. B. Chen and H. Chen}, Bifurcation diagram and global phase portraits of a family of quadratic vector fields in class $I$, Qual. Theory Dyn. Syst. { bf 19} (2020), no.~2, Paper No. 64, 22 pp.; MR4109532
- With name \(1S06\) 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 \(Fig 2.2 a\), \(Fig 2.2 b\) and \(Fig 2.2 d\) in {J. W. Reyn and R. E. Kooij}, Phase portraits of non-degenerate quadratic systems with finite multiplicity two, Differential Equations Dynam. Systems { bf 5} (1997), no.~3-4, 355--414; MR1660222Note (for name \(Fig 2.2 b\)): The system has 1 limit cycle.
- With name \(1S6\) 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.Note (for name \(1S6\)): notation should have to be 1.1L_1
Comments
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 \(QS132_{1}^{(2)}\) could potentially exhibit an additional limit cycle bifurcating from the focus.