\(QS8_{4}^{(0)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(8\) | \(4422\) | \(22\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = -x \, y+a \, (-1+2 \, x^{2}+y^{2}) \\ \dot{y} = -1+2 \, x^{2}+y^{2} \end{cases}\]
with parameters: \(a = 0.1\)
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 \(P17\) in {J. Llibre and R. D. S. Oliveira}, Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3, Nonlinear Anal. { bf 70} (2009), no. 12, 6378--6379.Note (for name \(P17\)): missed arrows
- With name \(S^2_{3,4}\) 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 \(QS37_{6}^{(1)}\), by means of a bifurcation of type \(A\), we reach the neighbor \(QS23_{1}^{(0)}\).
- Through the border \(QS8_{3}^{(1)}\), by means of a bifurcation of type \(D\), we reach the neighbor \(QS8_{3}^{(0)}\).
- Through the border \(QS8_{4}^{(1)}\), by means of a bifurcation of type \(D\), we reach the neighbor \(QS8_{5}^{(0)}\).
- Through the border \(QS11_{15}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS10_{13}^{(0)}\).
- Through the border \(QS11_{16}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS10_{13}^{(0)}\).
- Through the border \(QS11_{16}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS10_{14}^{(0)}\).
- Through the border \(QS11_{18}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS10_{14}^{(0)}\).
- Through the border \(QS11_{20}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS10_{16}^{(0)}\).