Grazing and border-collision in piecewise-smooth systems: A unified analytical framework

被引：145

作者：

di Bernardo, M ^{[1
]}

Budd, CJ

Champneys, AR

机构：

[1] Univ Bristol, Dept Engn Math, Bristol BS8 1TR, Avon, England

[2] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

来源：

PHYSICAL REVIEW LETTERS | 2001年 / 86卷 / 12期

关键词：

D O I：

10.1103/PhysRevLett.86.2553

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A comprehensive derivation is presented of normal form maps for grazing bifurcations in piecewise smooth models of physical processes. This links gratings 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.

引用

页码：2553 / 2556

页数：4

共 13 条

[1]

Brogliato B., 1999, NONSMOOTH MECH

[2] On the origin and bifurcations of stick-slip oscillations [J].

Dankowicz, H ;

Nordmark, AB .

PHYSICA D-NONLINEAR PHENOMENA, 2000, 136 (3-4) :280-302

[3] Instability, Subharmonics, and Chaos in Power Electronic Systems [J].

Deane, Jonathan H. B. ;

Hamill, David C. .

IEEE TRANSACTIONS ON POWER ELECTRONICS, 1990, 5 (03) :260-268

[4] Generic behavior of grazing impact oscillators [J].

deWeger, J ;

Binks, D ;

Molenaar, J ;

vandeWater, W .

PHYSICAL REVIEW LETTERS, 1996, 76 (21) :3951-3954

[5] Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems [J].

Di Bernardo, M ;

Feigin, MI ;

Hogan, SJ ;

Homer, ME .

CHAOS SOLITONS & FRACTALS, 1999, 10 (11) :1881-1908

[6]

di Bernardo M, 1998, NONLINEARITY, V11, P859, DOI 10.1088/0951-7715/11/4/007

[7]

DIBERNARDO M, 2000, 20003 ANM U BRIST

[8] Bifurcations caused by grazing incidence in many degrees of freedom impact oscillators [J].

Fredriksson, MH ;

Nordmark, AB .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1997, 453 (1961) :1261-1276

[9]

Keener J. P., 1998, MATH PHYSL

[10] NONPERIODIC MOTION CAUSED BY GRAZING-INCIDENCE IN AN IMPACT OSCILLATOR [J].

NORDMARK, AB .

JOURNAL OF SOUND AND VIBRATION, 1991, 145 (02) :279-297

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