\(QS38_{28}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(38\) | \(441\) | \(211111\) |
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 \(U^2_AD,68\) in {J. C. Artés}, Structurally unstable quadratic vector fields of codimension two: families possessing one finite saddle-node and a separatrix connection, Qual. Theory Dyn. Syst. { bf 23} (2024), no.~1, Paper No. 40, 88 pp.; MR4662466
- With names \(7S6\) and \(7S8\) 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)}Note (for name \(7S6\)): The system has 1 limit cycle.
- With name \(2.7L2\) in {J. C. Artés, J. Llibre and D. Schlomiuk}, The geometry of quadratic differential systems with a weak focus of second order, emph{ Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{16} (2006), {3127--3194}.
Comments
This phase portrait appears in J. C. Artés, J. Llibre and D. Schlomiuk (emph{ Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{16} (2006), {3127--3194}) featuring a weak focus of second order. Given that the portrait is of codimension 1, hyperbolic limit cycles can be generated without breaking its other unstable features. However, multiple limit cycle configurations are not guaranteed, as they might be incompatible with the pre-existing unstable properties of the system.