title: Grazing and border-collision in piecewise-smooth systems: a unified analytical framework.
abstract: A comprehensive derivation is presented of normal form maps for grazing bifurcations in piecewise smooth models of physical processes. This links grazings with border-collisions in nonsmooth maps. Contrary to previous literature, piecewise linear maps correspond only to nonsmooth discontinuity boundaries. All other maps have either square-root or (3/2)-type singularities.
authors: Department of Engineering Mathematics, University of Bristol, UK. M.diBernardo@bristol.ac.uk
authors: M
authors: M
authors: di Bernardo
authors: C J
authors: CJ
authors: Budd
authors: A R
authors: AR
authors: Champneys