\(QS68_{1}^{(4)}\)
Description
Phase Portrait
Topological Invariants
| TCSP |
|---|
| \(68\) |
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 \(14\) in {R. Benterki and J. Llibre}, Phase portraits of quadratic polynomial differential systems having as solution some classical planar algebraic curves of degree 4, Electron. J. Differential Equations { bf 2019}, Paper No. 15, 25 pp.; MR3919655
- With name \(X3\) in {C. A. Buzzi, J. Llibre and P. H. R. Santana}, Phase portraits of $(2;0)$ reversible vector fields with symmetrical singularities, J. Math. Anal. Appl. { bf 503} (2021), no.~2, Paper No. 125324, 21 pp.; MR42612202
- With name \(105\) in {B. Coll, A. Ferragut and J. Llibre}, Phase portraits of the quadratic systems with a polynomial inverse integrating factor, Internat. J. Bifur. Chaos Appl. Sci. Engrg. { bf 19} (2009), no.~3, 765--783; MR2533481
- With name \(4.5c\) 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 \(4.5c\)): wrong witdhs
- With name \(4,5c\) 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 \(40\) in {A. Ferragut, J. D. García-Saldaña and C. Valls}, Phase portraits of Abel quadratic differential systems of second kind with symmetries, Dyn. Syst. { bf 34} (2019), no.~2, 301--333; MR3941199Note (for name \(40\)): This needs 2 elliptic sectors
- With name \(P16\) in {J. Llibre and R. D. S. Oliveira}, Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3, Nonlinear Anal. { bf 70} (2009), no. 12, 6378--6379.
- With name \(Fig. 04\) in {J. Llibre and C. Pantazi}, Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 33 (2023), no. 1, Paper No. 2350003, 54 pp.
- With name \(28\) in {M. Ndiaye and H. J. Giacomini}, Quadratic systems equivalent by domains to a linear one: global phase portraits, Extracta Math. { bf 15} (2000), no.~1, 97--119; MR1792982
- With name \(Fig1.21 6\) in {K. S. Sibirskii}, Introduction to the algebraic theory of invariants of differential equations (Russian), ``Shtiintsa'', Kishinev, 1982; MR0716501
- With name \(fig 1.1(c)\) in {B. Coll, A. Gasull and J. Llibre}, Quadratic systems with a unique finite rest point, emph{Publ. Mat.}, textbf{32} (1988), 199--259.
- With name \(P16\) in {J. C. Artés, J. Llibre and N. Vulpe}, Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space $ Bbb R^{12$}, Rend. Circ. Mat. Palermo (2) { bf 59} (2010), no.~3, 419--449; MR2745521
- With names \(Fig5.3 I\) and \(Fig5.3 Iva\) 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.Note (for name \(Fig5.3 I\)): missed arrowNote (for name \(Fig5.3 Iva\)): missed arrow