\(QS75_{8}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(75\) | \(411\) | \(4121\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = P_x(x,y) \\ \dot{y} = P_y(x,y) \end{cases}\]
has the following phase portrait done with P4.
The phase portrait appears in the following papers
- With name \(U^2_{BC,11}\) in {J. C. Artés}, Systems of class BC2, {Preprint} (2026).
- With names \(5S05\), \(5S06\) and \(5S13\) in {J. C. Artés and L. Cairó}, Phase portraits of quadratic differential systems with a weak focus and a (1,1) SN, {Preprint} (2026).Note (for name \(5S06\)): The system has limit cycles with distribution \((0,1)\).Note (for name \(5S13\)): The system has limit cycles with distribution \((1,0)\).
- With name \(an15 Fig 2.33\) in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
Comments
This phase portrait appears in J. C. Artés and L. Cairó ({Preprint} (2026)) featuring a weak focus of first order. Consequently, a configuration structurally equivalent to \(QS75_{8}^{(2)}\) could potentially exhibit an additional limit cycle bifurcating from the focus.