Classification of dynamical systems based on a decomposition of their vector fields

Stavros Anastassiou, Spyros Pnevmatikos, Tassos Bountis

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We present a method for the global classification of dynamical systems based on a specific decomposition of their vector fields. Every differentiable vector field on Rn can be decomposed uniquely in the sum of 2 systems: one gradient and one that leaves invariant the spheres Sn-1. We show that, under some conditions, the topological class of a vector field is determined by the topological classes of its summands. We illustrate this method by applying it to a number of vector fields, among them being some members of the so-called Lorenz family. The advantage of such a classification is that equivalent flows exhibit qualitatively the same dynamical phenomena as their parameters are varied.

Original languageEnglish
Pages (from-to)2252-2262
Number of pages11
JournalJournal of Differential Equations
Volume253
Issue number7
DOIs
Publication statusPublished - Oct 1 2012
Externally publishedYes

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Vector Field
Dynamical systems
Dynamical system
Decomposition
Decompose
Differentiable
Gradient
Invariant
Class

ASJC Scopus subject areas

  • Analysis

Cite this

Classification of dynamical systems based on a decomposition of their vector fields. / Anastassiou, Stavros; Pnevmatikos, Spyros; Bountis, Tassos.

In: Journal of Differential Equations, Vol. 253, No. 7, 01.10.2012, p. 2252-2262.

Research output: Contribution to journalArticle

Anastassiou, Stavros ; Pnevmatikos, Spyros ; Bountis, Tassos. / Classification of dynamical systems based on a decomposition of their vector fields. In: Journal of Differential Equations. 2012 ; Vol. 253, No. 7. pp. 2252-2262.
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