\(QS10_{12}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(10\) | \(4410\) | \(311211\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = y+a \, x^{2}+b \, x \, y \\ \dot{y} = x^{2}+2 \, c \, x \, y+f \, y^{2}+d+e \, x+g \, (y+a \, x^{2}+b \, x \, y) \end{cases}\]
with parameters: \(a = 3, \quad b = 25, \quad c = \frac{73}{10}, \quad d = -0.0000001, \quad e = -0.0007, \quad f = c^2-1, \quad g = -0.0015\)
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 \(U^1_{D51}\) 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 \(QS10_{4}^{(0)}\) and \(QS10_{8}^{(0)}\).
Comments
If the stability of the focus inside the graphic is the opposite, we obtain portrait $QS010^1_2^C$ which is conjectured not to exist