Isoclines, critical points and classes of quadratic systems

Abstract

As was remarked before, a phase portrait is characterized by its critical points, separatrix structure and periodic solutions. In practice the analysis of a phase portrait usually starts with determination of the number, relative location and character of the critical points, both in the finite part of the plane and at infinity. This is so because, in itself, it contains vital information about the phase portrait, whereas it is also important for determination of the separatrix structure and the periodic solutions of the system at hand. As a result it seems natural, if classes of quadratic systems are to be defined, to base this on properties of the critical points, being the zero points of the vector field (P(x, y), Q(x,y)) in (1.0.1),(1.0.2).