Published: 31 December 2008

New concepts of nonlinear dynamics: protuberances, unstable periodic infinitiums and rare attractors

M. V. Zakrzhevsky1
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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-offreedom. 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

About this article

13 October 2008
02 December 2008
31 December 2008
dynamical system (DS)
complete bifurcation group
method of complete bifurcation group (MCBG)
unstable periodic infinitium (UPI)
rare attractors
strongly nonlinear driven systems
pendulum DS
impact DS
piecewise-linear DS