Application of the Method of Complete Bifurcation Groups in Parametrically Excited Pendulum Systems

An application of the new method of complete bifurcation groups (MCBG) in parametrically excited pendulum systems with an additional linear restoring moment and with the periodically vibrating point of suspension in both directions is introduced. Behaviour of the driven damped pendulum systems may be complex and with unexpected phenomena. Recent efforts in nonlinear dynamics show, that rare attractors (RA) have been found in all typical nonlinear models. Construction of complete bifurcation groups is based on the method of stable and unstable periodic regimes continuation on a parameter. This method is based on the ideas of Poincaré, Birkhoff, Andronov and others [6]. Global bifurcation analysis of the parametric pendulum systems allows to find new bifurcation groups, rare attractors and chaotic regimes. All results were obtained numerically, using our software