\(QS3_{2}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(3\) | \(4211\) | \(11\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = 1-x^{2}+2 \, y^{2} \\ \dot{y} = y \, (-20 \, x-21)/10 \end{cases}\]
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 \(A 4S3\) in {J. C. Artés, C. Bujac, D. Schlomiuk and N. Vulpe}, Phase portraits of real quadratic differential systems possessing an invariant ellipse, {Preprint} (2026).
- With name \(12\) in {R. Benterki and J. Llibre}, Phase portraits of quadratic polynomial differential systems having as solution some classical planar algebraic curves of degree 4, Electron. J. Differential Equations { bf 2019}, Paper No. 15, 25 pp.; MR3919655
- With name \(2\) 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 \(U^1_{D13}\) in {J. C. Artés, J. Llibre and A. C. Rezende}, Structurally unstable quadratic vector fields of codimension one, Birkhäuser/Springer, Cham, 2018, vi+267 pp.
- With name \(S IV 1\) in {J. C. Artés, J. Llibre, D. Schlomiuk and N. Vulpe}, Abel quadratic differential systems of second kind, Electron. J. Differential Equations { bf 2024}, Paper No. 50, 38 pp.; MR4793966
- With name \(V25\) 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.
Bifurcations in codimension 0
- Bifurcation interface between the codimension 0 portrait \(QS3_{1}^{(0)}\) and \(QS3_{1}^{(0)}\).
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 \(QS3_{2}^{(1)}\) could potentially exhibit an additional limit cycle bifurcating from the focus.