On a Behavior of Trajectories of a Certain Family of Cubic Dynamic Systems in a Poincare Circle

We present the results of the investigation of a family of dynamic systems on a real plane containing reciprocal cubic and square polynomials in their right parts. A Poincare method of serial mappings has been used. All possible for the systems under consideration topologically different types of phase portraits in a Poincare circle have been described and constructed. The total amount of such portraits appears to be over 200. Coefficient criteria of their realization have been outlined. (paper)