About Lyapunov characteristic indices

1Nikitina, NV
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2015, 8:64-71
https://doi.org/10.15407/dopovidi2015.08.064
Section: Mechanics
Language: Russian
Abstract: 

An approach to finding the Lyapunov characteristic indices is presented for the tasks of chaotic motions. The approach is based on the analysis of the bifurcations of points of a trajectory.

Keywords: bifurcation, nonlinear system, orbital loss of stability, strange attractor
References: 
  1. Neimark Yu. I., Landa P. S. Stochastic and Chaotic Oscillations, Dordrecht: Kluwer, 1992. https://doi.org/10.1007/978-94-011-2596-3
  2. Anishchenko V. S. Complex Oschillations in Simple Systems, Moscow: Nauka, 1990 (in Russian).
  3. Benettin G., Galgani I., Strelcyn J.M. Phys. Rev. A., 1976, 14, No 6: 2338–2345. https://doi.org/10.1103/PhysRevA.14.2338
  4. Shilnikov L.P., Shilnikov A. L., Turaev D.V., Chua L.O. Methods of Qualitative Theory in Nonlinear Dynamics. Part I., Singapore: World Scientific, 1998. https://doi.org/10.1142/9789812798596
  5. Leonov G.A. Strange Attractors and Classical Stability Theory, St.-Petersburg: University Press, 2008.
  6. Martynyuk A.A., Nikitina N.V. Int. Appl. Mech., 2015, 51, No 2: 540–541. https://doi.org/10.1007/s10778-015-0687-5
  7. Martynyuk A.A., Nikitina N.V. Nonlinear Oscillations, 2014, 17, No 2: 268–280.