\(QS10_{3}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(10\) | \(4431\) | \(211110\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = y+x^{2} \\ \dot{y} = e^{2} \, x/5-e \, y+x^{2}-y^{2} \end{cases}\]
with parameters: \(e = 0.582\)
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 \(Chap 3 15\) in {B. Imane and B. Souad}, Global phase portraits of quadratic differential systems exhibiting an invariant algebraic curve or an algebraic cubic first integral, {Ph.D. Universite Mohamed el Bachir}, (2020).Note (for name \(Chap 3 15\)): It is not clear if there is a separatrix connection. We assume it has
- With name \(U^1_{D42}\) 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 \(QS10_{10}^{(0)}\) and \(QS10_{14}^{(0)}\).