\(QS8_{1}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(8\) | \(4411\) | \(31\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = y+4 \, x^{2}-20 \, x \, y \\ \dot{y} = x^{2}+2 \, c \, x \, y+(c^{2}-1) \, y^{2}+b+a \, y \end{cases}\]
with parameters: \(a = -0.01, \quad b = -0.0000000001, \quad c = -2.15\)
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 \(U^1_{D2}\) 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 \(QS8_{2}^{(0)}\).