\(QS10_{6}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(10\) | \(4421\) | \(211210\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = x \, (-1/2+x+3 \, y/2) \\ \dot{y} = 2 \, y \, (1+x-y)+e \end{cases}\]
with parameters: \(e = -0.1\)
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 \(20\) in {A. Belfar and R. Benterki}, Qualitative dynamics of five quadratic polynomial differential systems exhibiting five classical cubic algebraic curves, Rend. Circ. Mat. Palermo (2) { bf 72} (2023), no.~1, 393--420; MR4543844
- With name \(2\) in {R. Benterki and A. Belfar}, Phase portraits of two classes of quadratic differential systems exhibiting as solutions two cubic algebraic curves, Demonstr. Math. { bf 56} (2023), no.~1, Paper No. 20220218, 16 pp.; MR4592893
- With name \(U^1_{D45}\) 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 \(Fig. 2 04\) and \(Fig. 2 08\) 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 (convex case), Qual. Theory Dyn. Syst. { bf 6} (2005), no.~2, 187--204; MR2420856
Bifurcations in codimension 0
- Bifurcation interface between the codimension 0 portrait \(QS10_{12}^{(0)}\) and \(QS10_{14}^{(0)}\).