Competing Dynamic Solutions in a Parametrically Excited Pendulum: Attractor Robustness and Basin Integrity

The competing solutions of a planar pendulum parametrically excited by the vertical motion of the pivot are investigated in terms of both attractor robustness and basin integrity. Two different measures are considered to highlight how the integrity of the system is modified by changing the amplitude of the excitation. Various attractors, both in-well and out-of-well, are considered, and the integrity profiles of each of them are determined. A detailed discussion of the interaction and mutual erosion of the various attractors is performed, by clarifying the role of the two complementary measures, and the most relevant characteristics of the erosion profiles are interpreted in terms of the underlying topological mechanisms involving local or global bifurcations.