Infinitely Remote Singularities of Special Differential Dynamic Systems

Year 2018, Issue: 4, 1 - 7, 04.12.2018

İrina Andreeva

https://izlik.org/JA99BN43EC

Abstract

The work is devoted to the results of a fundamental study on the
arithmetical plane of a broad special family of differential dynamic systems
having polynomial right parts. Let those polynomials be a cubic and a square
reciprocal forms. A task of a whole investigation was to find out all
topologically different phase portraits in a Poincare circle and indicate close
to coefficient criteria of them. To achieve this goal a Poincare method of the
central and the orthogonal consecutive displays (or mappings) has been used. As
a rezult more than 250 topologically different phase portraits
in a total have been constructed. Every portrait we depict with a special table
called a descriptive phase portrait. Each line of such a special table
corresponds to one invariant cell of the phase portrait and describes its
boundary, a source of its phase flow and a sink of it. All finite and
infinitely remote singularities of dynamic systems under consideration were
fully investigated. Namely infinitely remote singularities are discussed in the
present article.

Keywords

Dynamic systems , Phase portraits , Phase flows , Poincare sphere , Poincare circle , Singular points , Separatrices , Trajectories

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