Grazing and border-collision in piecewise-smooth systems: a unified analytical framework.
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.
di Bernardo
M
M
Department of Engineering Mathematics, University of Bristol, UK. M.diBernardo@bristol.ac.uk
Budd
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CJ
Champneys
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