Chattering bifurcations in a Duffing unilateral vibro-impact system

A tail-mapping is introduced to deal with the tail impacts caused by the chattering, and based on which, an effective numerical method is suggested to simulate the chattering in the vibro-impact system. As an illustrative example, a Duffing unilateral vibro-impact system is investigated. The results show the evidence of complete and incomplete chattering. We also investigate two novel chattering bifurcations, including transitions from complete to incomplete chattering and incomplete chattering period to aperiodic motion.