\(QS8_{7}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(8\) | \(4410\) | \(32\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = y+3 \, x^{2}+d \, x \, y \\ \dot{y} = x^{2}+2 \, e \, x \, y+(e^{2}-1) \, y^{2}+c+b \, y+a \, (y+3 \, x^{2}+d \, x \, y) \end{cases}\]
with parameters: \(b = 0.1, \quad c = -0.0000000001, \quad e = -1.1, \quad a = 0.005, \quad d = -7\)
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 \(U^1_{D8}\) 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.Note (for name \(U^1_{D8}\)): orbit inside the graphic must be attractor and rotate opposite
Bifurcations in codimension 0
- Bifurcation interface between the codimension 0 portrait \(QS8_{2}^{(0)}\) and \(QS8_{3}^{(0)}\).