We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector field there are exactly 25 different global phase portraits in the Poincaré disc, up to a reversal of sense. © 2006 Elsevier Ltd. All rights reserved.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 15 Jul 2007|
- Phase portraits
- Quadratic vector fields
- Rational first integral