\(QS094_1\)
Description
Phase Portrait
Topological Invariants
| TCSP |
|---|
| \(94\) |
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 \(P5\) in {J. C. Artés and C. Trullàs}, Quadratic Differential Systems with a Weak Focus of First-Order and a Finite Saddle-Node, {International Journal of Bifurcation and Chaos, Vol. 36, No. 6 (2026) 2630013 (99 pages)}
- With name \(P9\) 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; MR4906437
- With name \(29\) 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 \(D1S2\) 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.; MR4860323
- With name \(62\) 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 \(54\) 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 name \(B 4.8L5\) in {J. C. Artés, M. C. Mota and A. C. Rezende}, Quadratic systems possessing an infinite elliptic-saddle or an infinite nilpotent saddle, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 34} (2024), no.~11, Paper No. 2430023, 43 pp.; MR4801966
- With name \(w\) in {J. Llibre and M. F. da Silva}, Phase portraits of integrable quadratic systems with an invariant parabola and an invariant straight line, C. R. Math. Acad. Sci. Paris { bf 357} (2019), no.~2, 143--166; MR3927021
- With name \(P23\) in {J. Llibre and R. D. S. Oliveira}, Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3, Nonlinear Anal. { bf 70} (2009), no. 12, 6378--6379.
- With name \(2\) 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; MR1874098
- With name \(Fig 3 a\) 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 \(38\) in {M. Ndiaye and H. J. Giacomini}, Quadratic systems equivalent by domains to a linear one: global phase portraits, Extracta Math. { bf 15} (2000), no.~1, 97--119; MR1792982
- With name \(4.5L9\) 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 name \(Fig3b (1)\) in {J. W. Reyn}, Phase portraits of quadratic systems with finite multiplicity one, Nonlinear Anal. { bf 28} (1997), no.~4, 755--778; MR1420390
- With name \(E28\) in {B. Coll, A. Gasull and J. Llibre}, Quadratic systems with a unique finite rest point, emph{Publ. Mat.}, textbf{32} (1988), 199--259.
- With names \(Fig10.1 (10)\) and \(Fig10.4 (6)\) in {J. W. Reyn and X. H. Huang}, Phase portraits of quadratic systems with finite multiplicity three and a degenerate critical point at infinity, Rocky Mountain J. Math. { bf 27} (1997), no.~3, 929--978; MR1490285
- With name \(QS094_1\) 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).
- With name \(P23\) in {J. C. Artés, J. Llibre and N. Vulpe}, Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space $ Bbb R^{12$}, Rend. Circ. Mat. Palermo (2) { bf 59} (2010), no.~3, 419--449; MR2745521
- With name \(Vul13\) in {N. I. Vulpe}, Affine--invariant conditions for the topological distinction of quadratic systems with a center (in Russian), emph{Differentsial'nye Uravneniya}, textbf{19}, no. 3 (1983), 371--379. (Translation in emph{Differential Equations}, textbf{19} (1983), {273--280}.)