New Concepts of Nonlinear Dynamics: Complete Bifurcation Groups, Protuberances, Unstable Periodic Infinitiums and Rare Attractors

Journal of Vibroengineering 2008
Mihails Zakrževskis

A new approach for the global bifurcation analysis for strongly nonlinear dynamical systems, based on the ideas of Poincaré, Birkhoff and Andronov, is proposed. The main idea of the approach is a concept of complete bifurcation groups and periodic branch continuation along stable and unstable solutions, named by the author as a method of complete bifurcation groups (MCBG). The article is widely illustrated using archetypal dynamical systems with one-degree-of-freedom. Among them are: Duffing model (symmetrical, asymmetrical) with one and two potential wells, piecewise-linear systems with one and several potential wells, impact and pendulum systems.

Keywords
dynamical system (DS), bifurcation, complete bifurcation group, method of complete bifurcation group (MCBG), protuberance, unstable periodic infinitium (UPI), rare attractors, catastrophes, strongly nonlinear driven systems, pendulum DS, impact DS, piecewise-linear DS

Zakrževskis, M. New Concepts of Nonlinear Dynamics: Complete Bifurcation Groups, Protuberances, Unstable Periodic Infinitiums and Rare Attractors. Journal of Vibroengineering, 2008, Vol.10, Iss.4 , pp.421-441. ISSN 1392-8716.

Publication language
English (en)