From A. Tondl's Dutch contacts to Neimark-Sacker-bifurcation

Abstract

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.