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.
|Translated title of the contribution||Grazing and border-collision in piecewise-smooth systems: a unified analytical framework|
|Number of pages||4|
|Journal||Physical Review Letters|
|Publication status||Published - 19 Mar 2001|