\(QS11_{10}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(11\) | \(4411\) | \(4141\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = -e+x^{2}+2 \, h \, x \, y+(n-1-2 \, h) \, y^{2} \\ \dot{y} = -e \, c+y+c \, x^{2}+(2+2 \, h-2 \, c-n) \, x \, y+(c-2-2 \, h+2 \, n) \, y^{2} \end{cases}\]
with parameters: \(h = \frac{-21}{5}, \quad c = 3, \quad n = 10, \quad e = 0.00001\)
has the following phase portrait done with P4. If you want, you may download the P4 file here. Since the image is not clear enough, we have added a ZOOM of it.
The phase portrait appears in the following papers
- With names \(V044\) and \(V045\) in Missing reference in QWF1SN02Note (for name \(V045\)): The system has limit cycles with distribution \((1,0)\).
- With name \(U^1_{B18}\) 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.
Bifurcations in codimension 0
- Bifurcation interface between the codimension 0 portrait \(QS8_{3}^{(0)}\) and \(QS10_{8}^{(0)}\).