The Road to Chaotic and Rare Attractors in Damped Nonlinear Systems

Динамика виброударных (сильно нелинейных) систем DYVIS-2009 2009
Raisa Smirnova, Mihails Zakrževskis, Igors Ščukins, Vladislavs Jevstigņejevs

In this paper we consider new approaches for the research of the origin of chaotic oscillations and rare attractors based on the method of complete bifurcation groups. Typical element of the bifurcation group with a chaotic attractor is the area in parameter space with an infinite number of unstable periodic regimes, resulting from the cascade of period doubling bifurcations. Origin of rare attractors is inextricably linked to the chaotic oscillations of a particular bifurcation group, as illustrated on typical models of nonlinear systems with one and two degrees of freedom.

Keywords
Нелинейная динамика, метод полных бифуркационных групп, редкие и хаотические аттракторы

Smirnova, R., Zakrževskis, M., Ščukins, I., Jevstigņejevs, V. The Road to Chaotic and Rare Attractors in Damped Nonlinear Systems. In: Динамика виброударных (сильно нелинейных) систем DYVIS-2009, Russia, Москва – Звенигород, 24-30 May, 2009. Москва: ИМАШ РАН, 2009, pp.353-361. ISBN 978-5-904282-01-1. e-ISBN 5-904282-01-X.

Publication language
Russian (ru)