\(QS5_{5}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(5\) | \(4211\) | \(211011\) |
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: \(a = -0.1070380572094458, \quad c = 0.2385797474384179, \quad d = 0.04912509700465492, \quad g = 0.02864606566231576, \quad h = -0.07475789717196871, \quad k = 0.001752334387827448, \quad b = -0.05999020193164747, \quad e = 0.1478935208776219, \quad f = 0.08434033898844821, \quad l = 0.0168702900047177, \quad m = 0.08879440131167883, \quad n = -.2401536704624192, \quad s = -1.58\)
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 \(U^1_{D34}\) 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 \(QS5_{4}^{(0)}\) and \(QS5_{6}^{(0)}\).