\(QS86_{2}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(86\) | \(1\) | \(2120\) |
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 \(P28\) 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 name \(U^2_{BC,02}\) in {J. C. Artés}, Systems of class BC2, {Preprint} (2026).
- With name \(5S03\) in {J. C. Artés and L. Cairó}, Phase portraits of quadratic differential systems with a weak focus and a (1,1) SN, {Preprint} (2026).
- With names \(Fig1b (5)\) and \(Fig1b (9)\) in {J. W. Reyn}, Phase portraits of quadratic systems with finite multiplicity one, Nonlinear Anal. { bf 28} (1997), no.~4, 755--778; MR1420390Note (for name \(Fig1b (5)\)): The system has 1 limit cycle.
- With name \(in03 Fig 2.39\) in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
- With names \(E52\) and \(fig 5.14(e)=e12\) in {B. Coll, A. Gasull and J. Llibre}, Quadratic systems with a unique finite rest point, emph{Publ. Mat.}, textbf{32} (1988), 199--259.Note (for name \(fig 5.14(e)=e12\)): The system has 1 limit cycle.
- With name \(in03 Fig. 11\) in {J. W. Reyn and X. H. Huang}, Separatrix configurations of quadratic systems with finite multiplicity three and a $M^0_{1,1$ type of critical point at infinity}, Report U. Delft (1997?).
- With name \(1.5L2\) in {J. C. Artés, A. C. Rezende and R. Oliveira}, Global phase portraits of quadratic polynomial differential systems with a semi-elemental triple node, emph{Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, { bf 23}, no. 8 (2013), 1350140, 21 pp.
- With name \(1.2L7\) 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.
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 \(QS86_{2}^{(2)}\) could potentially exhibit an additional limit cycle bifurcating from the focus.