\(QS1_{6}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(1\) | \(4440\) | \(321211\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = c \, x+y+3 \, x \, y \\ \dot{y} = a+b \, x+x^{2}+x \, y/5-99/100 \, y^{2} \end{cases}\]
with parameters: \(a = -0.00000015, \quad b = -0.0007, \quad c = 0.000001\)
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 \(U^1_{D20}\) 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.Note (for name \(U^1_{D20}\)): orbit inside the graphic must be attractor and rotate opposite
- With name \(e_a(b)\) in {A. Zegeling}, Quadratic systems with three saddles and one antisaddle, Delft University of Technology, Faculty of Technical Mathematics and Informatics, Report 80 (1989). Note (for name \(e_a(b)\)): uncomplete case
Bifurcations in codimension 0
- Bifurcation interface between the codimension 0 portrait \(QS1_{3}^{(0)}\) and \(QS1_{4}^{(0)}\).