\(QS5_{1}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(5\) | \(4210\) | \(311011\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = y+a \, x^{2}+b \, x \, y \\ \dot{y} = x^{2}+2 \, c \, x \, y+(c^{2}-1) \, y^{2}+d+e \, x \end{cases}\]
with parameters: \(a = 3, \quad b = \frac{89}{10}, \quad c = 2, \quad d = -0.0000001, \quad e = -0.0007\)
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 name \(U^1_{D30}\) 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 \(QS5_{1}^{(0)}\) and \(QS5_{4}^{(0)}\).
Comments
If the stability of the focus inside the graphic is the opposite, we obtain portrait $QS005^1_1^C$ which is conjectured not to exist