\(QS32_{18}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(32\) | \(331\) | \(3121\) |
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 \(U^2_AB,70\) in {J. C. Artés, M. C. Mota and A. C. Rezende}, Structurally unstable quadratic vector fields of codimension two: families possessing a finite saddle-node and an infinite saddle-node, Electron. J. Qual. Theory Differ. Equ. { bf 2021}, Paper No. 35, 89 pp.; MR4252667
- With name \(5S31\) in {J. C. Artés and C. Trullàs}, Quadratic Differential Systems with a Weak Focus of First-Order and a Finite Saddle-Node, {International Journal of Bifurcation and Chaos, Vol. 36, No. 6 (2026) 2630013 (99 pages)}
- With names \(V137\) and \(V140\) in {J. C. Artés, A. C. Rezende and R. D. S. Oliveira}, The geometry of quadratic polynomial differential systems with a finite and an infinite saddle-node (C), emph{Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{25}, no. 3 (2015), 1530009, 111 pp.Note (for name \(V137\)): The system has limit cycles with distribution \((0,1)\).
Comments
This phase portrait appears in J. C. Artés and C. Trullàs ({International Journal of Bifurcation and Chaos, Vol. 36, No. 6 (2026) 2630013 (99 pages)}) featuring a weak focus of first order. Consequently, a configuration structurally equivalent to \(QS32_{18}^{(2)}\) could potentially exhibit an additional limit cycle bifurcating from the focus.