Saddle-point solutions and grazing bifurcations in an impacting system

This paper focuses on the intricate relationship between smooth and nonsmooth phenomena in an impacting system. In particular a boundary saddle-point solution, that is born in a nonsmooth fold, is analysed. Accessible boundary saddle-point solutions play a key role in determining the global dynamics of a system and here we will show how grazing bifurcations can affect their existence.