Geometric characteristics of cycles in some symmetric dynamical systems (In Russian)

by Andrey Akinshin, V P Golubyatnikov · 2012

Abstract

We show non-uniqueness of cycles in phase portraits of some odd-dimensional nonlinear dynamical systems considered as models of gene networks regulated by negative feedbacks. We find geometric and analytic characteristics of these cycles and construct a graph, which describes qualitative behavior of trajectories of these dynamical systems.

Reference

A A Akinshin, V P Golubyatnikov “Geometric characteristics of cycles in some symmetric dynamical systems (In Russian)" (2012)

@Article{akinshin2012nsu,
  abstract = {We show non-uniqueness of cycles in phase portraits of some odd-dimensional nonlinear dynamical systems considered as models of gene networks regulated by negative feedbacks. We find geometric and analytic characteristics of these cycles and construct a graph, which describes qualitative behavior of trajectories of these dynamical systems.},
  address = {Novosibirsk},
  author = {Akinshin, A A and Golubyatnikov, V P},
  institution = {NSU},
  issn = {1818-7897},
  journal = {Vestnik NSU [NSU Herald]. Series “Mathematics, mechanics, and informatics'”},
  custom-tags = {Vak},
  language = {russian},
  number = {2},
  pages = {3--12},
  title = {Geometric characteristics of cycles in some symmetric dynamical systems (In Russian)},
  url = {http://elibrary.ru/item.asp?id=18756520 http://www.mathnet.ru/php/archive.phtml?wshow=paper\&jrnid=vngu\&paperid=114\&option\_lang=eng},
  volume = {12},
  year = {2012}
}