Instability phenomena in impact damper system: From quasi-periodic motion to period-three motion

The instability phenomena of quasi-periodic attractor in the impact-damper system are reported in this paper. This special phenomena are found by accident when the Hopf bifurcation of impact periodic motion is studied in parameter plane. Quasi-periodic attractor is found to lose stability by sudden jump to period-three attractor or saddle-node bifurcation of period-three attractor on the invariant set. The MDCM (multi-DOF cell mapping) method is used to study the variety of attraction basins of solutions near the critical points of the jump phenomena. Spiral and fragmented attraction basins of solutions in a chosen two-dimensional subspace can be observed.