\(QS22_{2}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(22\) | \(11\) | \(1111\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = (cm \, x^{2})/10 - y + 2 \, ch \, x \, y \\ \dot{y} = x + (-2 \, ch + cl) \, x^{2} + (-cg + cm/10) \, x \, y + 2 \, ch \, y^{2} \end{cases}\]
has the following phase portrait done with P4. If you want, you may download the P4 file here.
The phase portrait appears in the following papers
- With name \(B12\) in {J. C. Artés and J. Llibre}, Phase portraits for quadratic systems having a focus and one anti-saddle, emph{Rocky Mountain J. Math.}, textbf{24} (1994), 875--889.
- With name \(BD12\) in {J. C. Artés}, Systems of class BD, {Preprint} (2026).
- With name \(29\) 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 \(P13\) 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 \(4S02\) in Missing reference in QWF1SN02
- With name \(Fig 1.33 b\) 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; MR1660222
- With name \(5S11\) 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.
Comments
This phase portrait appears in J. C. Artés, J. Llibre and D. Schlomiuk (emph{ Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{20}, no. 11 (2010), 3627--3662) featuring a weak focus of first order. Consequently, a configuration structurally equivalent to \(QS22_{2}^{(2)}\) could potentially exhibit an additional limit cycle bifurcating from the focus.