Multistability of a three-degree-of-freedom vibro-impact system

Four types of scenarios occurring multistability are identified in a vibro-impact system. Besides the coexistence of high-periodic attractors and chaotic attractors, this system has some coexisting multi-frequency quasiperiodical attractors. We observe the coexistence of different two-dimensional tori T2, which the mechanism of torus formation involves phase-locked dynamics on three-dimensional tori. We also find that the tori T3 and the tori T2 (or period-3) coexist for a certain set of parameters. The mechanism leading to the multistability is investigated through interplay among the codimension two bifurcations, strong resonance bifurcations and global bifurcations.