\(QS11_{1}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(11\) | \(4421\) | \(3211\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = -y-M \, x^{2}-L \, x \, y-N \, y^{2} \\ \dot{y} = x+A \, x \, y \end{cases}\]
with parameters: \(M = 1, \quad L = 3, \quad N = 1, \quad A = \frac{(L^2-4*M*N)}{(4*N)}\)
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 \(BD30\) in {J. C. Artés}, Systems of class BD, {Preprint} (2026).
- With name \(4S04\) in Missing reference in QWF1SN02
- With name \(5S9\) in {J. C. Artés, J. Llibre and D. Schlomiuk}, The geometry of quadratic polynomial differential systems with a weak focus and an invariant straight line, emph{ Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{20}, no. 11 (2010), 3627--3662.
Comments
This phase portrait appears in J. C. Artés, J. Llibre and D. Schlomiuk (emph{ Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{20}, no. 11 (2010), 3627--3662) featuring a weak focus of first order. Consequently, a configuration structurally equivalent to \(QS11_{1}^{(2)}\) could potentially exhibit an additional limit cycle bifurcating from the focus.