Analyzing phase portraits of quadratic systems

Abstract

As was mentioned in Chapter 1, this book aims at giving a survey of what has become known so far about the phase portraits of quadratic systems, thereby indicating what still has to be done to complete the picture on the subject. In order to approach this goal systematically, in the previous chapter non-degenerate quadratic systems were subdivided into 173 classes. For each class we now investigate what is known about its phase portraits and how to proceed to give a complete classification. In order to get an insight into the arguments and methods useful to obtain the topological character of a phase portrait, it is of interest to take into account general properties of quadratic systems and results obtained from studying classes of quadratic systems, characterized by a specific property.