Analytical investigation of single and double Neimark-Sacker bifurcations

  • Giuseppe Habib
  • Giuseppe Rega
  • Gábor Stépán

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.
Keywords: Neimark-Sacker bifurcation, double Neimark-Sacker, Near identity transformation, Center manifold reduction
How to Cite
Habib, G., Rega, G. and Stépán, G. (no date) “Analytical investigation of single and double Neimark-Sacker bifurcations”, Periodica Polytechnica Mechanical Engineering, 56(1), pp. 13-22. doi: https://doi.org/10.3311/pp.me.2012-1.03.
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Articles