\(QS168_{1}^{(6)}\)
Description
Phase Portrait
Topological Invariants
| TCSP |
|---|
| \(168\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = x \\ \dot{y} = d+b \, y+x^{2} \end{cases}\]
with parameters: \(b = 0, \quad d = -2\)
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 \(Fig 11 25\) in {L. Cairó and J. Llibre}, Phase portraits of Families VII and VIII of the Quadratic Systems. Axioms. No. 12(756), (2023), 18pp.
- With name \(7\) 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 \(4.38a\) 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 \(Fig 2 C-1L2\) 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 \(b\) in {J. Llibre and T. Salhi}, Planar quadratic differential systems with invariants of the form $ax^2+bxy+cy^2+d x+ey+c_1t$, Bull. Iranian Math. Soc. { bf 50} (2024), no.~4, Paper No. 49, 16 pp.; MR4755552
- With name \(Fig3 M^1_04,3(a)\) 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 \(Ric. 86\) 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 \(12\) 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 \(QS168_{1}^{(6)}\) 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).