\(QS25_{2}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(25\) | \(40\) | \(211101\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = y+a \, x^{2}+b \, x \, y+c \, x \\ \dot{y} = x^{2}+x \, y+y^{2}+d+e \, x+f \, (y+a \, x^{2}+b \, x \, y+c \, x) \end{cases}\]
with parameters: \(a = 0, \quad b = 2, \quad c = 0.001, \quad d = -0.00001, \quad e = -0.0007, \quad f = 0.0008\)
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 \(U^1_{D23}\) 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 \(QS25_{2}^{(0)}\) and \(QS25_{3}^{(0)}\).