메뉴 건너뛰기




Volumn 5, Issue 3, 2006, Pages 493-503

Dangerous border-collision bifurcations of a piecewise-smooth map

Author keywords

Border collision bifurcation; Chaos; Fixed points; Nonsmooth

Indexed keywords


EID: 33749411065     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2006.5.493     Document Type: Article
Times cited : (9)

References (15)
  • 1
    • 0035911618 scopus 로고    scopus 로고
    • Grazing and border-collision in piecewise-smooth systems: A unified analytical framework
    • M. di Bernardo, C.J. Budd and A.R. Champneys, Grazing and Border-Collision in Piecewise-Smooth Systems: A Unified Analytical Framework, Phys. Rev. Lett., 86 (2001), 2553.
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 2553
    • Di Bernardo, M.1    Budd, C.J.2    Champneys, A.R.3
  • 2
    • 0035892830 scopus 로고    scopus 로고
    • Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems
    • M. di Bernardo, C.J. Budd and A.R. Champneys, Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems, Physica D, 160 (2001), 222-254.
    • (2001) Physica D , vol.160 , pp. 222-254
    • Di Bernardo, M.1    Budd, C.J.2    Champneys, A.R.3
  • 3
    • 0033229544 scopus 로고    scopus 로고
    • Local analysis of C-bifurcations in n-dimensional piecewise-smooth dynamical systems
    • M. di Bernardo, M.I. Feigin, S.J. Hogan and M.E. Homer, Local Analysis of C-Bifurcations in n-Dimensional Piecewise-Smooth Dynamical Systems, Chaos, Solitons and Fractals, 10 (1999), 1881.
    • (1999) Chaos, Solitons and Fractals , vol.10 , pp. 1881
    • Di Bernardo, M.1    Feigin, M.I.2    Hogan, S.J.3    Homer, M.E.4
  • 4
    • 33749415561 scopus 로고    scopus 로고
    • Y. Do, preprint
    • Y. Do, preprint
  • 5
    • 0038351322 scopus 로고    scopus 로고
    • Multiple attractor bifurcations: A source of unpredictability in piecewise smooth systems
    • M. Dutta, H.E. Nusse, E. Ott, J.A. Yorke and G. Yuanb, Multiple Attractor Bifurcations: A Source of Unpredictability in Piecewise Smooth Systems, Phys. Rev. Lett., 83 (1999), 4281.
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 4281
    • Dutta, M.1    Nusse, H.E.2    Ott, E.3    Yorke, J.A.4    Yuanb, G.5
  • 8
    • 1642601666 scopus 로고    scopus 로고
    • Robust dangereuse border-collision bifurcation in piecewise smooth systems
    • M.A. Hassouneh, E.H. Abed and H.E. Nusse, Robust dangereuse border-collision bifurcation in piecewise smooth systems, Phy. Rev. Lett., 92 (2004), 070201.
    • (2004) Phy. Rev. Lett. , vol.92 , pp. 070201
    • Hassouneh, M.A.1    Abed, E.H.2    Nusse, H.E.3
  • 9
    • 14844336939 scopus 로고    scopus 로고
    • Robust chaos and border-collision bifurcations in non-invertible piecewise-linear maps
    • P. Kowalczyk, Robust chaos and border-collision bifurcations in non-invertible piecewise-linear maps, Nonlinearity, 18 (2005), 485-504.
    • (2005) Nonlinearity , vol.18 , pp. 485-504
    • Kowalczyk, P.1
  • 11
    • 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 Vib., 2 (1991), 279-297.
    • (1991) J. Sound Vib. , vol.2 , pp. 279-297
    • Nordmark, A.B.1
  • 12
    • 0001050846 scopus 로고
    • Border-collision bifurcations: An explanation for observed bifurcation phenomena
    • H.E. Nusse, E. Ott, and J.A. Yorke, Border-collision bifurcations: An explanation for observed bifurcation phenomena, Phys. Rev. E, 49 (1994), 1073.
    • (1994) Phys. Rev. E , vol.49 , pp. 1073
    • Nusse, H.E.1    Ott, E.2    Yorke, J.A.3
  • 13
    • 44049121950 scopus 로고
    • Border-collision bifurcation including "period two to period three" for piecewise smooth systems
    • H.E. Nusse and J.A. Yorke, Border-collision bifurcation 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, H.E.1    Yorke, J.A.2
  • 14
    • 0036925763 scopus 로고    scopus 로고
    • B order-collision bifurcations at the change of state-space dimension
    • S. Parui and S. Banerjee, B order-collision bifurcations at the change of state-space dimension, Chaos, 12 (2002), 1054-1069.
    • (2002) Chaos , vol.12 , pp. 1054-1069
    • Parui, S.1    Banerjee, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.