\(QS8_{6}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(8\) | \(4420\) | \(31\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = y-2 \, x \, y \\ \dot{y} = x^{2}+4 \, x \, y+3 \, y^{2}+e+d \, y \end{cases}\]
with parameters: \(d = 0.1, \quad e = -0.0012\)
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 \(Fig. 29\) in {J. Llibre and C. Pantazi}, Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023), no. 1, Paper No. 2350003, 54 pp.
- With name \(U^1_{D7}\) 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 \(QS8_{1}^{(0)}\) and \(QS8_{5}^{(0)}\).