On motions in a small neighborhood of zero of a multidimensional system

1Nikitina, NV
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 6:49-57
Section: Mechanics
Language: Russian
Abstract: 

The qualitative analysis of singular points of multidimensional systems is given. In three-dimensional systems (base models) that form attractors, the special points at zero can be saddle-headed or septofocus. In the bundle of two oscillators (Duffing and Van der Pol), the sum of characteristic indices at a singular point with syn ch ro nization is zero.

Keywords: bifurcation, nonlinear multidimensional system
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