PARAMETRICALLY EXCITED PENDULUM SYSTEMS WITH SEVERAL EQUILIBRIUM POSITIONS: BIFURCATION ANALYSIS AND RARE ATTRACTORS

Abstract

An application of the new method of complete bifurcation groups (MCBG) in parametrically excited pendulum systems with several equilibrium positions and with the periodically vibrating point of suspension in both directions is introduced. Construction of complete bifurcation groups is based on the method of stable and unstable periodic regimes continuation on a parameter. Global bifurcation analysis of the parametrically excited pendulum systems with several equilibrium positions allows finding new bifurcation groups with rare attractors and chaotic regimes.