\(QS10_{5}^{(0)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(10\) | \(4422\) | \(312110\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = -y \, (1+y-m \, x)+b \, x \, (1+a \, x) \\ \dot{y} = x \, (1+a \, x) \end{cases}\]
with parameters: \(m = \frac{-a+1}{a}, \quad a = \frac{n-1}{2}, \quad b = 0.3, \quad n = 0.1\)
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 \(S^2_{10,05}\) 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 \(QS11_{6}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS8_{1}^{(0)}\).
- Through the border \(QS76_{3}^{(1)}\), by means of a bifurcation of type \(C\), we reach the neighbor \(QS1_{2}^{(0)}\).
- Through the border \(QS38_{10}^{(1)}\), by means of a bifurcation of type \(A\), we reach the neighbor \(QS25_{1}^{(0)}\).
- Through the border \(QS38_{11}^{(1)}\), by means of a bifurcation of type \(A\), we reach the neighbor \(QS25_{1}^{(0)}\).
- Through the border \(QS38_{12}^{(1)}\), by means of a bifurcation of type \(A\), we reach the neighbor \(QS25_{1}^{(0)}\).
- Through the border \(QS10_{1}^{(1)}\), by means of a bifurcation of type \(D(a)\), we reach the neighbor \(QS10_{3}^{(0)}\).
- Through the border \(QS10_{2}^{(1)}\), by means of a bifurcation of type \(D\), we reach the neighbor \(QS10_{6}^{(0)}\).
- Through the border \(QS74_{6}^{(1)}\), by means of a bifurcation of type \(C\), we reach the neighbor \(QS5_{3}^{(0)}\).