\(QS76_{2}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(76\) | \(442\) | \(111111\) |
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 \(PP12\) in {J. C. Artés, J. Llibre and Huaxin Ou}, Quadratic systems with two invariant straight lines and an invariant hyperbola, {Preprint} (2026).
- With name \(Fig 10 2\) in {Y. Bolaños, J. Llibre and C. Valls}, Phase portraits of quadratic Lotka-Volterra systems with a Darboux invariant in the Poincaré disc, Commun. Contemp. Math. { bf 16} (2014), no.~6, 1350041, 23 pp.; MR3277950
- With name \(CD30\) in {J. C. Artés}, Systems of class CD, {Preprint} (2026).
- With names \(Fig 2 8\) and \(Fig 2 22\) in {P. C. Carri\~ao, M. E. S. Gomes and A. A. G. Ruas}, Planar quadratic vector fields with two or three finite singularities and a finite saddle connection on a straight line, Qual. Theory Dyn. Syst. { bf 8} (2009), no.~1, 25--44; MR2575806Note (for name \(Fig 2 8\)): wrong arrow
- With name \(3,5(g1)\) in {D. Schlomiuk and N. Vulpe}, Global classification of the planar Lotka--Volterra differential systems according to their configurations of invariant straight lines, emph{J. Fixed Point Theory Appl.}, { bf 8}, no. 1 (2010), 177--245.
- With name \(Fig1.b\) in {J. Llibre and C. Valls}, Global dynamics of a system coming from the study of a static star, Differ. Equ. Dyn. Syst. { bf 32} (2024), no.~2, 607--617; MR4721747
- With name \(PP01\) in {J. Llibre and H. X. Ou}, Quadratic systems with two invariant real straight lines and an invariant hyperbola, {Preprint} (2026).
- With name \(ap06 Fig 2.63\) in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
- With name \(ap06 Fig. 34\) in {J. W. Reyn and X. H. Huang}, Separatrix configurations of quadratic systems with finite multiplicity three and a $M^0_{1,1$ type of critical point at infinity}, Report U. Delft (1997?).
- With names \(Fig3.1 A1\) and \(Fig3.1 A2\) in {J. W. Reyn}, Phase portraits of a quadratic system of differential equations occurring frequently in applications, emph{Nieuw Arch. Wisk. (4)}, textbf{5}, no. 2 (1987), 107--151.