Bifurcations of Oscillatory and Rotational Solutions of Double Pendulum with Parametric Vertical Excitation
Figure 2
Bifurcation diagrams of oscillations: the double pendulum (Figure 1) in two-parameter space . (a) Diagram representing 1 : 1 : 1 resonance. The thick lines apart from the black one represent saddle-node bifurcation, while the thin lines represent period doubling. (b) One-parameter space (, ) continuation for : thick line represents stable solution, while dashed line represents unstable solution. (c) Diagram representing 2 : 1 : 1 resonance. (d) One-parameter space continuation for , red, , blue, and , black. Abbreviations of bifurcations: SN: saddle-node, PD: period doubling, and SB: symmetry breaking.
