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

Mario Di Bernardo; Christopher J Budd; Alan R Champneys

doi:10.1103/PhysRevLett.86.2553

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

Mario Di Bernardo, Christopher J Budd, Alan R Champneys

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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 contribution	Grazing and border-collision in piecewise-smooth systems: a unified analytical framework
Original language	English
Pages (from-to)	2553-2556
Number of pages	4
Journal	Physical Review Letters
Volume	86
Issue number	12
DOIs	https://doi.org/10.1103/PhysRevLett.86.2553
Publication status	Published - 19 Mar 2001

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Publisher: American Physical Society

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Engineering Mathematics Research Group

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10.1103/PhysRevLett.86.2553

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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.",

author = "{Di Bernardo}, Mario and Budd, {Christopher J} and Champneys, {Alan R}",

note = "Publisher: American Physical Society",

year = "2001",

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doi = "10.1103/PhysRevLett.86.2553",

language = "English",

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T1 - Grazing and Border-Collision in Piecewise-Smooth Systems

T2 - A Unified Analytical Framework

AU - Di Bernardo, Mario

AU - Budd, Christopher J

AU - Champneys, Alan R

N1 - Publisher: American Physical Society

PY - 2001/3/19

Y1 - 2001/3/19

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevLett.86.2553

DO - 10.1103/PhysRevLett.86.2553

M3 - Article (Academic Journal)

SN - 0031-9007

VL - 86

SP - 2553

EP - 2556

JO - Physical Review Letters

JF - Physical Review Letters

IS - 12

ER -

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

Abstract

Bibliographical note

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