A broad family of differential dynamic systems is considered on
a real plane of their phase variables x, y. The main common feature of systems
under consideration is the follows: every particular system includes two
equations with polynomial right parts of the third order in one equation and of
the second order in another one. These polynomials are mutually reciprocal in
the following understanding: their decomposition into forms of lower order does
not contain common multipliers. The whole family of such dynamic systems has
been split into subfamilies according to numbers of different multipliers in
the abovementioned decomposition and depending on an order of sequence of
different roots of polynomials. Every subfamily has been studied in a Poincare
circle using especially developed investigation methods. As a result all
possible for the dynamic systems belonging to this family phase portraits have
been revealed and described. There appeared to exist more than 200 different
topological types of phase portraits in a Poincare circle. The obtained results
have a scientific interest as well as a methodical and educational one.
Primary Language | English |
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Subjects | Engineering |
Journal Section | Articles |
Authors | |
Publication Date | August 19, 2018 |
Published in Issue | Year 2018Issue: 2 |