Analytical investigation of single and double Neimark-Sacker bifurcations

Giuseppe Habib, Giuseppe Rega, G. Stépán

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The analytical investigation of bifurcations is a very challenging task for many applied scientists and engineers. Often, numerical simulations cannot clarify the complicated dynamics of mechanical systems, in this cases, preprogrammed softwares can be of valid help during the investigation. Also, in the literature, methodology to study bifurcations are presented for most of the cases. However, the presented procedures, are often very hard to be understood from applied scientists with low mathematical background. In this paper we present in details the typical procedure to analyze single and double Neimark-Sacker bifurcations. Especially regarding the double Neimark-Sacker bifurcations of maps, very few sources can be found in the literature, although this kind of bifurcation is very common in many dynamical systems.

Original languageEnglish
Pages (from-to)13-22
Number of pages10
JournalPeriodica Polytechnica, Mechanical Engineering
Volume56
Issue number1
DOIs
Publication statusPublished - 2012

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Bifurcation (mathematics)
Dynamical systems
Engineers
Computer simulation

Keywords

  • Center manifold reduction
  • Double Neimark-Sacker
  • Near identity transformation
  • Neimark-Sacker bifurcation

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Analytical investigation of single and double Neimark-Sacker bifurcations. / Habib, Giuseppe; Rega, Giuseppe; Stépán, G.

In: Periodica Polytechnica, Mechanical Engineering, Vol. 56, No. 1, 2012, p. 13-22.

Research output: Contribution to journalArticle

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