Resumen de Separatrices
Temple H. Fay, Stephan Joubert
In this article we examine 2 × 2 first-order systems of ordinary differential equations and show how to identify separatrices for phase plane portraits when the system has a saddle point critical value. We describe how to use a computer algebra system to generate trajectories from contour plots, when possible, and determine the equation of the separatrix. When this approach is not possible, we describe how to use numerical investigations to determine the separatrix. Generating a phase plane portrait is useful, for at a glance one can observe what initial values give rise to bounded solutions, periodic solutions and other important features. It also permits the instructor to concentrate on the qualitative aspects of the model under investigation rather than the calculational difficulties associated with finding solutions. A list of examples suitable for student study is given in an appendix.
