\(QS37_{9}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(37\) | \(541\) | \(31\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = (1-e) \, x^{2}+2 \, h \, x \, y+(n-1-2 \, h) \, y^{2} \\ \dot{y} = y+c \, (1-e) \, x^{2}+(2+2 \, h-n) \, (1-e) \, x \, y-2 \, c \, x \, y+(c-2-2 \, h+2 \, n) \, y^{2} \end{cases}\]
with parameters: \(h = \frac{481}{2000}, \quad c = -10, \quad n = 1, \quad e = -0.001\)
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 \(A 2S03\) in {J. C. Artés, C. Bujac, D. Schlomiuk and N. Vulpe}, Phase portraits of real quadratic differential systems possessing an invariant ellipse, {Preprint} (2026).
- With name \(U^1_{A10}\) 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.
- With name \(5S33\) in {J. C. Artés, A. C. Rezende and R. D. S. Oliveira}, The geometry of quadratic polynomial differential systems with a finite and an infinite saddle-node (C), emph{Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{25}, no. 3 (2015), 1530009, 111 pp.
Bifurcations in codimension 0
- Bifurcation interface between the codimension 0 portrait \(QS23_{1}^{(0)}\) and \(QS8_{5}^{(0)}\).