\(QS002_1\)
Description
Phase Portrait
Topological Invariants
| TCSP | Fin Sep | Inf Sep |
|---|---|---|
| \(2\) | \(4440\) | \(211211\) |
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 \(Chap 2 1\) in {B. Imane and B. Souad}, Global phase portraits of quadratic differential systems exhibiting an invariant algebraic curve or an algebraic cubic first integral, {Ph.D. Universite Mohamed el Bachir}, (2020).
- With name \(99\) 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 \(6\) in {B. García, J. Llibre and J. S. Pérez del Río}, Phase portraits of the quadratic vector fields with a polynomial first integral, Rend. Circ. Mat. Palermo (2) { bf 55} (2006), no.~3, 420--440; MR2287071
- With name \(vulpe8\) in {J. C. Artés and J. Llibre}, Quadratic Hamiltonian vector fields, emph{J. Differential Equations}, { bf 107} (1994), 80--95.
- With name \(Vul 8\) in {J. C. Artés, J. Llibre and N. Vulpe}, Quadratic systems with an integrable saddle: A complete classification in the coefficient space $ mathbb{R^{12}$}, emph{Nonlinear Anal.}, textbf{75}, no. 14 (2012), 5416--5447.
- With names \(Fig. 1 11\) and \(Fig. 8 4\) in {P. C. Carri\~ao, M. E. S. Gomes and A. A. G. Ruas}, Planar quadratic vector fields with finite saddle connection on a straight line (non-convex case), Qual. Theory Dyn. Syst. { bf 7} (2009), no.~2, 417--433; MR2486684
- With name \(Vul8\) in {N. I. Vulpe}, Affine--invariant conditions for the topological distinction of quadratic systems with a center (in Russian), emph{Differentsial'nye Uravneniya}, textbf{19}, no. 3 (1983), 371--379. (Translation in emph{Differential Equations}, textbf{19} (1983), {273--280}.)
- With name \(c^a_1(b)\) in {A. Zegeling}, Quadratic systems with three saddles and one antisaddle, Delft University of Technology, Faculty of Technical Mathematics and Informatics, Report 80 (1989). Note (for name \(c^a_1(b)\)): uncomplete case