\(QS7_{5}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(7\) | \(4211\) | \(4121\) |
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: \(h = -5, \quad c = 6, \quad n = 10, \quad e = \frac{1}{10000}\)
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 \(V025\), \(V026\) and \(V048\) in Missing reference in QWF1SN02Note (for name \(V025\)): The system has limit cycles with distribution \((0,1,0)\).Note (for name \(V048\)): The system has limit cycles with distribution \((0,0,1)\).
- With name \(U^1_{B37}\) 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 \(QS3_{1}^{(0)}\) and \(QS5_{5}^{(0)}\).