Phase portraits of quadratic polynomial differential systems having as solution some classical planar algebraic curves of degree 4

Benterki, RebihaLlibre, Jaume2021-10-152021-10-152019-01-28Benterki, R., & Llibre, J. (2019). Phase portraits of quadratic polynomial differential systems having as solution some classical planar algebraic curves of degree 4. <i>Electronic Journal of Differential Equations, 2019</i>(15), pp. 1-25.1072-6691https://hdl.handle.net/10877/14658We classify the phase portraits of quadratic polynomial differential systems having some relevant classic quartic algebraic curves as invariant algebraic curves, i.e. these curves are formed by orbits of the quadratic polynomial differential system. More precisely, we realize 16 different well-known algebraic curves of degree 4 as invariant curves inside the quadratic polynomial differential systems. These realizations produce 31 topologically different phase portraits in the Poincare disc for such quadratic polynomial differential systems.Text25 pages1 file (.pdf)enAttribution 4.0 InternationalQuadratic differential systemPoincare discInvariant algebraic curvePhase portraits of quadratic polynomial differential systems having as solution some classical planar algebraic curves of degree 4ArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.