\(QS169_{1}^{(6)}\)
Description
Phase Portrait
Topological Invariants
| TCSP |
|---|
| \(169\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = x^{2} \\ \dot{y} = d+b \, y+x^{2}+m \, x \, y \end{cases}\]
with parameters: \(d = 4, \quad b = 1, \quad m = 1\)
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 \(1\) in {B. Coll, A. Ferragut and J. Llibre}, Phase portraits of the quadratic systems with a polynomial inverse integrating factor, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 19} (2009), no.~3, 765--783; MR2533481
- With name \(4.46\) in {D. Schlomiuk and N. Vulpe}, Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four, emph{Bul. Acad. c{S}tiin c{t}e Repub. Mold. Mat.}, { bf 1 (56)} (2008), 27--83.
- With name \(Fig 1 B1-5S1\) in {J. C. Artés, L. Cairó and J. Llibre}, New Exploration of Phase portraits Classification of QuadraticPolynomial Differential Systems based on Invariant Theory. Applied Math. No. 1(0), (2025), 24pp.
- With name \(Fig3 M^1_04,3(c)\) in {J. W. Reyn}, Phase portraits of quadratic systems without finite critical points, Nonlinear Anal. { bf 27} (1996), no.~2, 207--222; MR1389478
- With name \(Ric. 87\) in {J. C. Artés, J. Llibre, D. Schlomiuk and N. Vulpe}, Global analysis of Riccati quadratic differential systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 34} (2024), no.~1, Paper No. 2450004, 46 pp.; MR4701478
- With name \(13\) in {A. Gasull, S. Li Ren and J. Llibre}, Chordal quadratic systems, emph{Rocky Mountain J. Math.}, textbf{16}, no. 4 (1986), 751--782.
- With name \(QS169_{1}^{(6)}\) in {J. C. Artés, J. Llibre, D. Schlomiuk and N. Vulpe}, Phase portraits of a family of real quadratic differential systemspossessing a nilpotent or intricate singularity at infinity, {Preprint} (2026).