\(QS5_{4}^{(0)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(5\) | \(4311\) | \(311011\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = y+2 \, x^{2}+3 \, x \, y \\ \dot{y} = e^{2} \, x/5-e \, y+x^{2}+5 \, x \, y/2+9 \, y^{2}/16 \end{cases}\]
with parameters: \(e = 0.2\)
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 \(S^2_{12,4}\) in {J. C. Artés, R. E. Kooij and J. Llibre}, Structurally stable quadratic vector fields, Mem. Amer. Math. Soc. { bf 134} (1998), no.~639, viii+108 pp.; MR1432139
Neighbours of Codimension 1
- Through the border \(QS7_{4}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS3_{1}^{(0)}\).
- Through the border \(QS74_{8}^{(1)}\), by means of a bifurcation of type \(C\), we reach the neighbor \(QS10_{9}^{(0)}\).
- Through the border \(QS74_{7}^{(1)}\), by means of a bifurcation of type \(C\), we reach the neighbor \(QS10_{10}^{(0)}\).
- Through the border \(QS31_{8}^{(1)}\), by means of a bifurcation of type \(A\), we reach the neighbor \(QS19_{1}^{(0)}\).
- Through the border \(QS31_{9}^{(1)}\), by means of a bifurcation of type \(A\), we reach the neighbor \(QS19_{1}^{(0)}\).
- Through the border \(QS5_{1}^{(1)}\), by means of a bifurcation of type \(D(b)\), we reach the neighbor \(QS5_{1}^{(0)}\).
- Through the border \(QS5_{5}^{(1)}\), by means of a bifurcation of type \(D(d)\), we reach the neighbor \(QS5_{6}^{(0)}\).
- Through the border \(QS5_{9}^{(1)}\), by means of a bifurcation of type \(D\), we reach the neighbor \(QS5_{7}^{(0)}\).
Comments
No limit cycle is known in this portrait. There is the challenge to see if any of the antisaddles which receive just one separatrix may have a limit cycle.