Phase portraits of a special class of dynamic systems in a Poincare circle

Abstract

In this paper, authors present results of the original investigation of a special class of dynamic systems with the reciprocal polynomial –cubic and square – right parts on a real plane. The global task was to construct all topologically different phase portraits in a Poincare circle with criteria of them. For such an aim a Poincare method of a central and orthogonal mappings has been used. Eventually above the two hundred of different phase portraits were constructed. Each and every portrait has been described in a table. Each line of a table describes one invariant cell of the phase portrait under consideration, its boundary, a source of its phase flow and a sink of it.