Title:	From A.Tondl’s Dutch contacts to Neimark-Sacker-bifurcation
Authors:	Bakri, Taoufik Verhulst, Ferdinand
Citation:	Applied and Computational Mechanics. 2022, vol. 16, no. 2, p. 87-100.
Issue Date:	2022
Publisher:	University of West Bohemia
Document type:	článek article
URI:	http://hdl.handle.net/11025/50894
ISSN:	1802-680X (Print) 2336-1182 (Online)
Keywords:	Tondl;Neimark-Sackerova bifurkace;parametrické buzení;samobuzení;kvaziperiodické řešení
Keywords in different language:	Tondl;Neimark-Sacker bifurcation;parametric excitation;self-excitation;quasiperiodic solution
Abstract in different language:	We present a description of the many contacts of A. Tondl with Dutch scientists involving nonlinear dynamics models for mechanics. One of the topics is Neimark-Sacker bifurcation that leads to the presence of families of quasi-periodic solutions that are geometrically organised and visualised in tori. A new model in the spirit of A. Tondl, containing interaction of self-excited and parametrically excited oscillators is analysed to find this bifurcation and quasi-periodic solutions. The analysis using averaging in combination with numerical bifurcation tools Matcont and Auto produces a picture of rich dynamical phenomena with several surprises among which a special quasi-periodic solution produced by the averaged equation.
Rights:	© University of West Bohemia
Appears in Collections:	Volume 16, number 2 (2022) Volume 16, number 2 (2022)

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