Discontinuity-induced bifurcations in models of mechanical contact, capillary adhesion, and cell division: A common framework

This paper collects four distinct instances of grazing contact of a periodic trajectory in a hybrid dynamical system under a common abstract framework and establishes selected general properties of the associated near-grazing dynamics. In particular, it is shown that for critical choices of parameter values, commonly used physical models of rigid or compliant mechanical contact, capillary adhesion, and cell division satisfy the conditions...