Grazing-induced chaostic crisis for periodic orbits in vibro-impact systems

A numerical approximation of grazing manifold is proposed via the digraph cell mapping method. The global dynamics of grazing-induced crisis for a typical Duffing vibro-impact system are then investigated. The results reveal that, the singularity caused by the grazing nature of periodic orbits can induce a bifurcation where a periodic saddle and a chaotic saddle arise simultaneously. When the stable and unstable manifolds of the periodic saddle undergo the tangency, a boundary crisis occurs and a chaotic attractor is then brought from the chaotic saddle. Also, grazing phenomenon of periodic orbits induced by noise can be observed. This grazing phenomenon can induce a novel interior crisis, where a chaotic attractor arises due to the collision of this periodic attractor and the chaotic saddle.