\(QS1_{1}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(1\) | \(4442\) | \(212111\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = x \, (-1+x+2 \, y/3) \\ \dot{y} = y \, (1-2 \, x-y) \end{cases}\]
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 \(PP14\) in {J. C. Artés, J. Llibre and Huaxin Ou}, Quadratic systems with two invariant straight lines and an invariant hyperbola, {Preprint} (2026).
- With name \(3.1(a1)\) 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 \(Fig1.c\) 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 \(PP04\) in {J. Llibre and H. X. Ou}, Quadratic systems with two invariant real straight lines and an invariant hyperbola, {Preprint} (2026).
- With name \(U^1_{D15}\) 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 names \(Fig. 1 01\), \(Fig. 1 20\), \(Fig. 3 1\), \(Fig. 3 3\), \(Fig. 4 1\), \(Fig. 4 8\), \(Fig. 5 1\), \(Fig. 5 7\), \(Fig. 6 1\), \(Fig. 6 8\), \(Fig. 7 1\), \(Fig. 7 8\), \(Fig. 8 1\), \(Fig. 8 7\), \(Fig. 9 1\) and \(Fig. 9 8\) in {P. C. Carri\~ao, M. E. S. Gomes and A. A. G. Ruas}, Planar quadratic vector fields with finite saddle connection on a straight line (non-convex case), Qual. Theory Dyn. Syst. { bf 7} (2009), no.~2, 417--433; MR2486684
- With names \(Fig 2A V\) and \(Fig 2A XIII\) 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.
- With name \(c_3\) in {A. Zegeling}, Quadratic systems with three saddles and one antisaddle, Delft University of Technology, Faculty of Technical Mathematics and Informatics, Report 80 (1989).
Bifurcations in codimension 0
- Bifurcation interface between the codimension 0 portrait \(QS1_{1}^{(0)}\) and \(QS1_{2}^{(0)}\).