Attractors of 3D Systems in Basic Models of Mechanics*

The theorems (statements) on the existence of attractor are proved. A generalized Shilnikov theorem is formulated. In the expression for the saddle of a homoclinic loop, it includes an additional term that has a qualitative value in the formation of a strange attractor. A bifurcation program for the synchronization of 3D coupled identical generators is considered. The cause of new motions appearing in coupled generators is established.

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Correspondence to N. V. Nikitina.

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Translated from Prikladnaya Mekhanika, Vol. 56, No. 5, pp. 89–108, September–October 2020.

This research is funded from the budget program “Support for the Priority Areas of Research” (KPKVK 6541230).

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Nikitina, N.V. Attractors of 3D Systems in Basic Models of Mechanics*. Int Appl Mech 56, 599–617 (2020). https://doi.org/10.1007/s10778-020-01038-2

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Keywords

  • two-disk dynamo model
  • attractor
  • bifurcation
  • strange attractor
  • symmetry principles
  • synchronization
  • multistable system