Method of Complete Bifurcation Groups and its Application in Nonlinear Dynamics

2009
Mihails Zakrževskis, Raisa Smirnova, Igors Ščukins, Vladislavs Jevstigņejevs, Viktors Kugelevičs, Valentīns Frolovs, Aleksejs Klokovs, Eduards Šilvāns

A new approach for the global bifurcation analysis of strongly nonlinear dynamical systems is under consideration. The main idea of the approach is a concept of complete bifurcation groups and periodic branch continuation along stable and unstable solutions, named as a method of complete bifurcation groups (MCBG). In this paper it is shown that using MCBG allows to find new nonlinear effects and unknown before periodic (rare attractors) and chaotic regimes in archetypal dynamical systems with one- and two-degrees-of-freedom: bilinear, pendulum, rotor dynamics, with several equilibrium positions, negative damping.

Atslēgas vārdi
Nonlinear dynamics, method of complete bifurcation groups, rare attractors, chaos, archetypal dynamical systems with one- and two-degrees-of-freedom

Zakrževskis, M., Smirnova, R., Ščukins, I., Jevstigņejevs, V., Kugelevičs, V., Frolovs, V., Klokovs, A., Šilvāns, E. Method of Complete Bifurcation Groups and its Application in Nonlinear Dynamics. Mehānika. Nr.31, 2009, 27.-34.lpp. ISSN 1407-8015.

Publikācijas valoda
English (en)