The Transition to Chaos and Criteria of Chaotic Behavior in Dynamical Systems with Linear and Nonlinear Damping

Международная школа молодых ученых "Нелинейная динамика машин" (School-NDM). XVII Симпозиум "Динамика виброударных (сильно нелинейных) систем" (DYVIS-2012) : сборник трудов 2012
Raisa Smirnova

The achieved result is the elaboration of the basic theory for searching chaotic oscillations and nonlinear effects based on the concepts of periodic skeletons, complete bifurcation groups and method of rare attractors. The chaotic attractor possesses the characteristic amount of periodic skeletons and order of bifurcation groups. The approach allows us to forecast and to find new groups with rare catastrophic or rare useful phenomena with chaotic attractors in the nonlinear driven systems with linear and nonlinear damping. The results of work can be used in the engineering recommendations on how to use complex periodic, chaotic and rare attractors in the engineering systems for the purpose of favorable usage of nonlinear effects in the vibro-technology. It can also be used to forecast catastrophic situations and chaotic oscillations in the mechanics or other nonlinear dynamic systems.

Keywords
bifurcation, complete bifurcation groups method, chaos, linear and nonlinear damping

Smirnova, R. The Transition to Chaos and Criteria of Chaotic Behavior in Dynamical Systems with Linear and Nonlinear Damping. In: Международная школа молодых ученых "Нелинейная динамика машин" (School-NDM). XVII Симпозиум "Динамика виброударных (сильно нелинейных) систем" (DYVIS-2012) : сборник трудов, Russia, Moscow-Klin, 20-26 May, 2012. Москва: РАН, 2012, pp.261-267. ISBN 978-5-904282-03-5.

Publication language
English (en)