\(QS7_{8}^{(2)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(7\) | \(4321\) | \(1111\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = -y-M \, x^{2}-L \, x \, y-N \, y^{2} \\ \dot{y} = x+A \, x \, y \end{cases}\]
with parameters: \(M = -0.9, \quad L = 1, \quad N = 1, \quad A = 1.15\)
has the following phase portrait done with P4. If you want, you may download the P4 file here.
The phase portrait appears in the following papers
- With name \(BD24\) in {J. C. Artés}, Systems of class BD, {Preprint} (2026).
- With name \(3,9(b3)\) in {D. Schlomiuk and N. Vulpe}, Global classification of the planar Lotka--Volterra differential systems according to their configurations of invariant straight lines, emph{J. Fixed Point Theory Appl.}, { bf 8}, no. 1 (2010), 177--245.
- With name \(4S05\) in Missing reference in QWF1SN02
- With name \(5S10\) in {J. C. Artés, J. Llibre and D. Schlomiuk}, The geometry of quadratic polynomial differential systems with a weak focus and an invariant straight line, emph{ Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{20}, no. 11 (2010), 3627--3662.
- With names \(Fig 2B VI-VII\) and \(Fig 2D XI-XII\) in {J. W. Reyn}, Phase portraits of a quadratic system of differential equations occurring frequently in applications, emph{Nieuw Arch. Wisk. (4)}, textbf{5}, no. 2 (1987), 107--151.
Comments
This phase portrait appears in J. C. Artés, J. Llibre and D. Schlomiuk (emph{ Internat. J. Bifur. Chaos Appl. Sci. Engrg.}, textbf{20}, no. 11 (2010), 3627--3662) featuring a weak focus of first order. Consequently, a configuration structurally equivalent to \(QS7_{8}^{(2)}\) could potentially exhibit an additional limit cycle bifurcating from the focus.