Open AccessPhase portraits of a special class of dynamic systems in a Poincare circle
Author(s) -
İrina Andreeva,
Tatiana Efimova
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1236/1/012053
Subject(s) - phase portrait , poincaré conjecture , portrait , poincaré map , mathematics , class (philosophy) , square (algebra) , pure mathematics , geometry , computer science , physics , bifurcation , art history , artificial intelligence , art , quantum mechanics , nonlinear system
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.