\(QS76_{10}^{(1)}\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(76\) | \(443\) | \(211111\) |
Example
The quadratic differential system
\[\begin{cases} \dot{x} = x+a \, y+e \, y^{2}+d \, (m \, x+g \, y+x \, y) \\ \dot{y} = m \, x+g \, y+x \, y \end{cases}\]
with parameters: \(a = 2, \quad e = 1, \quad d = 0, \quad m = 1, \quad g = 1\)
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 \(Fig 10 4\) in {Y. Bolaños, J. Llibre and C. Valls}, Phase portraits of quadratic Lotka-Volterra systems with a Darboux invariant in the Poincaré disc, Commun. Contemp. Math. { bf 16} (2014), no.~6, 1350041, 23 pp.; MR3277950
- With name \(4.4a\) in {D. Schlomiuk and N. Vulpe}, Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four, emph{Bul. Acad. c{S}tiin c{t}e Repub. Mold. Mat.}, { bf 1 (56)} (2008), 27--83.Note (for name \(4.4a\)): missed arrow
- With names \(4,4a\), \(3,4(g3)\) and \(3,5(g2)\) 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 \(P04\) in {J. Llibre and C. Valls}, Global phase portraits for the Abel quadratic polynomial differential equations of second kind with $Z_2$-symmetries, Canad. Math. Bull. { bf 61} (2018), no.~1, 149--165; MR3746481
- With name \(U^1_{C14}\) in {J. C. Artés, J. Llibre and A. C. Rezende}, Structurally unstable quadratic vector fields of codimension one, Birkhäuser/Springer, Cham, 2018, vi+267 pp.
- With name \(ap07 Fig 2.63\) in {X. Huang}, Qualitative analysis or certain nonlinear differential equations, {Ph.D. U. Delft}, (1996).
- With name \(ap07 Fig. 34\) 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 names \(Fig3.1 B5\), \(Fig3.1 C3\) and \(Fig3.3 IX\) 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.
Bifurcations in codimension 0
- Bifurcation interface between the codimension 0 portrait \(QS1_{1}^{(0)}\) and \(QS10_{16}^{(0)}\).