\(QS5_{7}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(5\) | \(4211\) | \(111111\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = a+c \, x+d \, y+g \, x^{2}+h \, x \, y+k \, y^{2}+s \, (b+e \, x+f \, y+l \, x^{2}+m \, x \, y+n \, y^{2}) \\ \dot{y} = b+e \, x+f \, y+l \, x^{2}+m \, x \, y+n \, y^{2} \end{cases}\]
with parameters: \(a = 0, \quad c = -0.1625717331076329, \quad d = -0.04221485681339095, \quad g = -0.1195710610283694, \quad h = 0.2567025288715270, \quad k = -0.1306381546925663, \quad b = 0, \quad e = 0.2041440422516498, \quad f = 0.08282501653371581, \quad l = 0, \quad m = -0.1401146623718601, \quad n = 0.1466079755224514, \quad s = 0.172\)
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 \(U^1_{D36}\) 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 \(QS5_{6}^{(0)}\) and \(QS5_{7}^{(0)}\).