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Qualitative theory of two-dimensional polynomial dynamical systems

Authors
  • Shestopalov, Yury
  • Shakhverdiev, Azizaga
Publication Date
Jan 01, 2021
Identifiers
DOI: 10.3390/sym13101884
OAI: oai:DiVA.org:hig-37169
Source
DiVA - Academic Archive On-line
Keywords
Language
English
License
Green
External links

Abstract

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes.

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