\(QS85_{2}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(85\) | \(0\) | \(111010\) |
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 \(CD06\) in {J. C. Artés}, Systems of class CD, {Preprint} (2026).
- With names \(7S01\) and \(7S02\) 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 \(7S02\)): The system has 1 limit cycle.
- With name \(Fig1b (7)\) in {J. W. Reyn}, Phase portraits of quadratic systems with finite multiplicity one, Nonlinear Anal. { bf 28} (1997), no.~4, 755--778; MR1420390
- With name \(1.7L5\) 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}.
- With name \(E34=e8\) in {B. Coll, A. Gasull and J. Llibre}, Quadratic systems with a unique finite rest point, emph{Publ. Mat.}, textbf{32} (1988), 199--259.
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.