Grazing and Border-Collision in Piecewise-Smooth Systems: A Unified Analytical Framework

Mario Di Bernardo, Christopher J Budd, Alan R Champneys

Research output: Contribution to journalArticle (Academic Journal)peer-review

149 Citations (Scopus)
254 Downloads (Pure)

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.
Translated title of the contributionGrazing and border-collision in piecewise-smooth systems: a unified analytical framework
Original languageEnglish
Pages (from-to)2553-2556
Number of pages4
JournalPhysical Review Letters
Volume86
Issue number12
DOIs
Publication statusPublished - 19 Mar 2001

Bibliographical note

Publisher: American Physical Society

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