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Co-dimension-one grazing bifurcations of 1 / n impact periodic motions are often accompanied by saddle-node bifurcations or period-doubling bifurcations. The presence of certain degenerate grazing bifurcation points plays an important role in transitions between these two different co-dimension-one grazing bifurcation scenarios. When the saddle-node bifurcation line and period-doubling bifurcation...
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...
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