Higher order zero time discontinuity mapping for analysis of degenerate grazing bifurcations of impacting oscillators

The discontinuity mapping technique provides quite a good way to study the near-grazing dynamics in the impacting oscillators. However, disagreements between the results obtained by the discontinuity mapping technique and the direct numerical observations still exist in terms of modeling and stability analysis. In particular, when applying the existing theory to deal with the complicated degenerate or other co-dimension two grazing bifurcations,...