What are P4&P5 programs?

P4 and P5 are computer programs which study specific Polynomial Planar Vector Fields (or Differential System) of any degree. Both plot the phaseportrait of a vector field in the Poincaré disk.

Part of the calculations are done through an interface with the computer program Maple (giving the option of treating a vector field using symbolic manipulations), and part of them by the program itself.

A piecewise vector field is a finite number of vector fields defined on a domains that are bounded by a finite number of algebraic curves (bifurcation lines).  Such vector fields are often found in control theory.  The piecewise polynomial vector fields can be discontinuous along the bifurcation lines.

P5 is an extension of P4, and is introduced to be able to treat such piecewise vector fields.  Much of the functionality of P5 is inherited by P4.

Chapters 9 and 10 of the book Qualitative theory of planar differential systems (F. Dumortier, J. Llibre, J. C. Artés. Springer-Verlag, Berlin, 2006 ISBN 9783540328933) contains a complete description of how P4 works and what you can do with it.


  • Joan C. Artés. Universitat Autònoma de Barcelona.
  • Peter de Maesschalck. Hasselt University.
  • Freddy Dumortier. Hasselt University.
  • Chris Herssens. Hassel University.
  • Jaume Llibre, Universitat Autònoma de Barcelona.
  • Oscar Saleta. Universitat Autònoma de Barcelona.
  • Joan Torregrosa. Universitat Autònoma de Barcelona.