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Volumn 160, Issue 3-4, 2001, Pages 222-254

Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems

Author keywords

Discontinuity mapping; Dynamical systems; Grazing bifurcations

Indexed keywords


EID: 0035892830     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(01)00349-9     Document Type: Article
Times cited : (213)

References (44)
  • 1
    • 85120115251 scopus 로고    scopus 로고
    • B. Brogliato, Impacts in mechanical systems—analysis and modelling, in: Lecture Notes in Physics, Vol. 551, Springer, New York, 2000.
  • 2
    • 85120122079 scopus 로고    scopus 로고
    • J. Deane, D. Hamill, Analysis, simulation and experimental study of chaos in the buck converter, in: Proceedings of the Power Electronics Specialists Conf. (PESC 1990), IEEE Press, New York, 1990, pp. 491–498.
  • 3
    • 85120136725 scopus 로고    scopus 로고
    • S. Norsworthy, R. Schreier, G. Temes, Delta–Sigma Data Converters—Theory, Design, and Simulation, IEEE Press, New York, 1997.
  • 4
    • 0001353153 scopus 로고
    • Chattering and related behaviour in impact oscillators
    • C. Budd F. Dux Chattering and related behaviour in impact oscillators Phil. Trans. R. Soc. London A 347 1994 365 389
    • (1994) Phil. Trans. R. Soc. London A , vol.347 , pp. 365-389
    • Budd, C.1    Dux, F.2
  • 5
    • 80055018858 scopus 로고
    • Theoretical analysis of n-multiple (1/n)-impact solutions
    • F. Peterka Theoretical analysis of n -multiple (1/ n )-impact solutions CSAV Acta Technica 26 2 1974 462 473
    • (1974) CSAV Acta Technica , vol.26 , Issue.2 , pp. 462-473
    • Peterka, F.1
  • 6
    • 0030105497 scopus 로고    scopus 로고
    • A piecewise linear suspension bridge model: nonlinear dynamics and orbit continuation
    • S. Doole S. Hogan A piecewise linear suspension bridge model: nonlinear dynamics and orbit continuation Dynamics Stability Syst. 11 1996 19 29
    • (1996) Dynamics Stability Syst. , vol.11 , pp. 19-29
    • Doole, S.1    Hogan, S.2
  • 7
    • 0029754178 scopus 로고    scopus 로고
    • Study of chaos in the buck converter. I. Fundamental Theory and Applications
    • E. Fossas G. Olivar Study of chaos in the buck converter. I. Fundamental Theory and Applications IEEE Trans. Circuits Syst. 43 1996 13 25
    • (1996) IEEE Trans. Circuits Syst. , vol.43 , pp. 13-25
    • Fossas, E.1    Olivar, G.2
  • 8
    • 0001369548 scopus 로고
    • On the dynamics of rigid-block motion under harmonic forcing
    • S. Hogan On the dynamics of rigid-block motion under harmonic forcing Proc. R. Soc. London A 425 1989 441 476
    • (1989) Proc. R. Soc. London A , vol.425 , pp. 441-476
    • Hogan, S.1
  • 9
    • 0025416905 scopus 로고
    • Passive dynamic walking
    • T. McGeer Passive dynamic walking Int. J. Robotics Res. 9 1990 62 82
    • (1990) Int. J. Robotics Res. , vol.9 , pp. 62-82
    • McGeer, T.1
  • 10
    • 51249163979 scopus 로고
    • Dynamical behaviour of friction oscillators with simultaneous self and external excitation
    • K. Popp N. Hinrichs M. Oestreich Dynamical behaviour of friction oscillators with simultaneous self and external excitation Sadhana Indian Acad. Sci. 20 1995 627 654
    • (1995) Sadhana Indian Acad. Sci. , vol.20 , pp. 627-654
    • Popp, K.1    Hinrichs, N.2    Oestreich, M.3
  • 11
    • 0033229544 scopus 로고    scopus 로고
    • Local analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems
    • M. di Bernardo M. Feigin S. Hogan M. Homer Local analysis of C -bifurcations in n -dimensional piecewise smooth dynamical systems Chaos Solitons Fractals 10 1999 1881 1908
    • (1999) Chaos Solitons Fractals , vol.10 , pp. 1881-1908
    • di Bernardo, M.1    Feigin, M.2    Hogan, S.3    Homer, M.4
  • 12
    • 0000780796 scopus 로고    scopus 로고
    • Border collision bifurcations in two-dimensional piecewise smooth maps
    • S. Banerjee C. Grebogi Border collision bifurcations in two-dimensional piecewise smooth maps Phys. Rev. E 59 1999 4052 4061
    • (1999) Phys. Rev. E , vol.59 , pp. 4052-4061
    • Banerjee, S.1    Grebogi, C.2
  • 13
    • 0026419524 scopus 로고
    • Non-periodic motion caused by grazing incidence in impact oscillators
    • A.B. Nordmark Non-periodic motion caused by grazing incidence in impact oscillators J. Sound Vibration 2 1991 279 297
    • (1991) J. Sound Vibration , vol.2 , pp. 279-297
    • Nordmark, A.B.1
  • 14
    • 49849107837 scopus 로고
    • Doubling of the oscillation period with C-bifurcations in piecewise continuous systems
    • M. Feigin Doubling of the oscillation period with C -bifurcations in piecewise continuous systems Prikladnaya Matematika Mekhanica (J. Appl. Math. Mech.) 34 1970 861 869
    • (1970) Prikladnaya Matematika Mekhanica (J. Appl. Math. Mech.) , vol.34 , pp. 861-869
    • Feigin, M.1
  • 15
    • 0000516779 scopus 로고
    • On the generation of sets of subharmonic modes in a piecewise continuous system
    • M. Feigin On the generation of sets of subharmonic modes in a piecewise continuous system Prikladnaya Matematika Mekhanica (J. Appl. Math. Mech.) 38 1974 810 818
    • (1974) Prikladnaya Matematika Mekhanica (J. Appl. Math. Mech.) , vol.38 , pp. 810-818
    • Feigin, M.1
  • 16
    • 0000736695 scopus 로고
    • On the structure of C-bifurcation boundaries of piecewise continuous systems
    • M. Feigin On the structure of C -bifurcation boundaries of piecewise continuous systems Prikiadnaya Matematika Mekhanica (J. Appl. Math. Mech.) 42 1978 820 829
    • (1978) Prikiadnaya Matematika Mekhanica (J. Appl. Math. Mech.) , vol.42 , pp. 820-829
    • Feigin, M.1
  • 17
    • 85120144860 scopus 로고    scopus 로고
    • V. Babitskii, Theory of Vibroimpact Systems. Approximate Methods, Nauka, Moscow, 1978.
  • 18
    • 0009370405 scopus 로고
    • Periodically forced linear oscillator with impacts: chaos and long-periodic motions
    • S. Shaw P. Holmes Periodically forced linear oscillator with impacts: chaos and long-periodic motions Phys. Rev. Lett. 51 1983 623 626
    • (1983) Phys. Rev. Lett. , vol.51 , pp. 623-626
    • Shaw, S.1    Holmes, P.2
  • 19
    • 0028516064 scopus 로고
    • Bifurcations in impact oscillators
    • S. Foale S. Bishop Bifurcations in impact oscillators Nonlinear Dynamics 6 1994 285 299
    • (1994) Nonlinear Dynamics , vol.6 , pp. 285-299
    • Foale, S.1    Bishop, S.2
  • 20
    • 0023648094 scopus 로고
    • The vibro-impact response of a harmonically excited and preloaded one-dimensional linear oscillator
    • G. Whiston The vibro-impact response of a harmonically excited and preloaded one-dimensional linear oscillator J. Sound Vibrations 115 1987 303 324
    • (1987) J. Sound Vibrations , vol.115 , pp. 303-324
    • Whiston, G.1
  • 21
    • 0041822709 scopus 로고    scopus 로고
    • Grazing, skipping and sliding: analysis of the nonsmooth dynamics of the dc/dc buck converter
    • M. di Bernardo C. Budd A. Champneys Grazing, skipping and sliding: analysis of the nonsmooth dynamics of the dc/dc buck converter Nonlinearity 11 1998 858 890
    • (1998) Nonlinearity , vol.11 , pp. 858-890
    • di Bernardo, M.1    Budd, C.2    Champneys, A.3
  • 23
    • 0000208406 scopus 로고
    • Grazing bifurcations in impact oscillators
    • W. Chin E. Ott H. Nusse C. Grebogi Grazing bifurcations in impact oscillators Phys. Rev. E 50 1994 4427 4444
    • (1994) Phys. Rev. E , vol.50 , pp. 4427-4444
    • Chin, W.1    Ott, E.2    Nusse, H.3    Grebogi, C.4
  • 24
    • 0000501202 scopus 로고
    • Analytical determination of bifurcations in an impact oscillator
    • S. Foale Analytical determination of bifurcations in an impact oscillator Phil. Trans. R. Soc. London A 347 1994 353 364
    • (1994) Phil. Trans. R. Soc. London A , vol.347 , pp. 353-364
    • Foale, S.1
  • 25
    • 0002883084 scopus 로고
    • Intermittency in impact oscillators close to resonance
    • C. Budd F. Dux Intermittency in impact oscillators close to resonance Nonlinearity 7 1994 1191 1224
    • (1994) Nonlinearity , vol.7 , pp. 1191-1224
    • Budd, C.1    Dux, F.2
  • 26
    • 0001019656 scopus 로고
    • Chaotic dynamics of an impact oscillator
    • J. Thompson R. Ghaffari Chaotic dynamics of an impact oscillator Phys. Rev. A 27 1983 1741 1743
    • (1983) Phys. Rev. A , vol.27 , pp. 1741-1743
    • Thompson, J.1    Ghaffari, R.2
  • 27
    • 0002035723 scopus 로고    scopus 로고
    • On normal form calculations in impact oscillators
    • M. Frederiksson A. Nordmark On normal form calculations in impact oscillators Proc. R. Soc. London A 456 2000 315 329
    • (2000) Proc. R. Soc. London A , vol.456 , pp. 315-329
    • Frederiksson, M.1    Nordmark, A.2
  • 28
    • 85120146618 scopus 로고    scopus 로고
    • M. Feigin, Forced Oscillations in Systems with Discontinuous Nonlinearities, Nauka, Moscow, 1994 (in Russian).
  • 29
    • 21344472534 scopus 로고
    • The increasingly complex structure of the bifurcation tree of a piecewis smooth system
    • M. Feigin The increasingly complex structure of the bifurcation tree of a piecewis smooth system Prikladnaya Matematika Mekhanica (J. Appl. Math. Mech.) 59 1995 853 863
    • (1995) Prikladnaya Matematika Mekhanica (J. Appl. Math. Mech.) , vol.59 , pp. 853-863
    • Feigin, M.1
  • 30
    • 44049121950 scopus 로고
    • Border-collision bifurcations including period two to period three for piecewise smooth systems
    • L. Nusse J. Yorke Border-collision bifurcations including period two to period three for piecewise smooth systems Physica D 57 1992 39 57
    • (1992) Physica D , vol.57 , pp. 39-57
    • Nusse, L.1    Yorke, J.2
  • 31
    • 0001050846 scopus 로고
    • Border collision bifurcation: an explanation for observed bifurcation phenomena
    • L. Nusse J. Yorke Border collision bifurcation: an explanation for observed bifurcation phenomena Phys. Rev. E 49 1994 1073 1076
    • (1994) Phys. Rev. E , vol.49 , pp. 1073-1076
    • Nusse, L.1    Yorke, J.2
  • 32
    • 4344639901 scopus 로고
    • Border ollision bifurcations for piecewise smooth on dimensional maps
    • L. Nusse J. Yorke Border ollision bifurcations for piecewise smooth on dimensional maps Int. J. Bifurcation Chaos 5 1995 189 207
    • (1995) Int. J. Bifurcation Chaos , vol.5 , pp. 189-207
    • Nusse, L.1    Yorke, J.2
  • 34
    • 0021097823 scopus 로고
    • A periodically forced piecewise linear oscillator
    • S. Shaw P. Holmes A periodically forced piecewise linear oscillator J. Sound Vibration 90 1983 129 144
    • (1983) J. Sound Vibration , vol.90 , pp. 129-144
    • Shaw, S.1    Holmes, P.2
  • 35
    • 33746715031 scopus 로고    scopus 로고
    • Bifuractions caused by grazing incidence in many degrees of freedom impact oscillators
    • M. Frederiksson A. Nordmark Bifuractions caused by grazing incidence in many degrees of freedom impact oscillators Proc. R. Soc. London A 453 1997 1261 1276
    • (1997) Proc. R. Soc. London A , vol.453 , pp. 1261-1276
    • Frederiksson, M.1    Nordmark, A.2
  • 36
    • 4244118801 scopus 로고    scopus 로고
    • Universal limit mapping in grazing bifurcatious
    • A. Nordmark Universal limit mapping in grazing bifurcatious Phys. Rev. E 55 1997 266 270
    • (1997) Phys. Rev. E , vol.55 , pp. 266-270
    • Nordmark, A.1
  • 37
    • 0346688041 scopus 로고    scopus 로고
    • On the origin and bifurcations of stick-slip oscillations
    • H. Dankowicz A. Nordmark On the origin and bifurcations of stick-slip oscillations Physica D 136 1999 280 302
    • (1999) Physica D , vol.136 , pp. 280-302
    • Dankowicz, H.1    Nordmark, A.2
  • 38
    • 0035911618 scopus 로고    scopus 로고
    • Grazing and border-collision in piecewise smooth systems: a unified analytical framework
    • M. di Bernardo C. Budd A. Champneys Grazing and border-collision in piecewise smooth systems: a unified analytical framework Phys. Rev. Lett. 86 2001 2553 2556
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 2553-2556
    • di Bernardo, M.1    Budd, C.2    Champneys, A.3
  • 39
    • 85120108950 scopus 로고    scopus 로고
    • A. Filippov, Differential Equations with Discontinuous Righthand Sides, Kluwer Academic Publishers, Dortrecht, 1988.
  • 40
    • 85120109429 scopus 로고    scopus 로고
    • M. di Bernardo, P. Kowalczyk, A. Nordmark, Bifurcations in dynamical systems with sliding: derivation of normal form maps, 2001, Physica D, submitted.
  • 41
    • 85120115587 scopus 로고    scopus 로고
    • Ya.Z. Tsypkin, Relay Control Systems, CUP, Cambridge, UK, 1984.
  • 42
    • 85120146757 scopus 로고    scopus 로고
    • M. di Bernardo, C. Budd, A. Champneys, Corner-collision implies border collision bifurcation, Physica D 154 (2001) 171–194.
  • 43
    • 85120126997 scopus 로고    scopus 로고
    • M. di Bernardo, K. Johansson, F. Vasca, Self-oscillations and sliding in relay feedback systems: Symmetry and bifurcations, Int. J. Bifurcations Chaos 11 (4) (2001) 1121–1140.


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