메뉴 건너뛰기




Volumn 55, Issue 3, 2009, Pages 239-250

Fractional derivative reconstruction of forced oscillators

Author keywords

Chaos; Embeddings; Fractional calculus; Fractional derivatives; Phase space reconstructions

Indexed keywords

DERIVATIVES; FRACTAL DIMENSION; FUNCTIONS; OSCILLATORS (ELECTRONIC); PHASE SPACE METHODS; REPAIR;

EID: 58149147615     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-008-9359-x     Document Type: Article
Times cited : (12)

References (43)
  • 1
    • 0000779360 scopus 로고
    • Detecting strange attractors in turbulence
    • Springer Berlin
    • Takens, F.: Detecting strange attractors in turbulence. In: Lecture Notes in Mathematics, vol. 898, pp. 366-381. Springer, Berlin (1981)
    • (1981) Lecture Notes in Mathematics , vol.898 , pp. 366-381
    • Takens, F.1
  • 3
    • 0010162362 scopus 로고
    • The Takens embedding theorem
    • 4
    • L. Noakes 1991 The Takens embedding theorem Int. J. Bifurc. Chaos 1 4 867 872
    • (1991) Int. J. Bifurc. Chaos , vol.1 , pp. 867-872
    • Noakes, L.1
  • 4
    • 34548696055 scopus 로고
    • Independent coordinates for strange attractors from mutual information
    • 2
    • A.M. Fraser H.L. Swinney 1986 Independent coordinates for strange attractors from mutual information Phys. Rev. A 33 2 1134 1140
    • (1986) Phys. Rev. A , vol.33 , pp. 1134-1140
    • Fraser, A.M.1    Swinney, H.L.2
  • 5
    • 35949006791 scopus 로고
    • Determining embedding dimension for phase-space reconstruction using a geometrical construction
    • M. Kennel R. Brown H.D.I. Abarbanel 1992 Determining embedding dimension for phase-space reconstruction using a geometrical construction Phys. Rev. A 45 3403 3411
    • (1992) Phys. Rev. A , vol.45 , pp. 3403-3411
    • Kennel, M.1    Brown, R.2    Abarbanel, H.D.I.3
  • 6
    • 0001874436 scopus 로고    scopus 로고
    • Practical method for determining the minimum embedding dimension of a scalar time series
    • L. Cao 1997 Practical method for determining the minimum embedding dimension of a scalar time series Physica D 110 43 50
    • (1997) Physica D , vol.110 , pp. 43-50
    • Cao, L.1
  • 7
    • 0001762008 scopus 로고    scopus 로고
    • Distortions of reconstruction for chaotic attractors
    • A. Potopov 1997 Distortions of reconstruction for chaotic attractors Physica D 101 207 226
    • (1997) Physica D , vol.101 , pp. 207-226
    • Potopov, A.1
  • 8
    • 0042020821 scopus 로고
    • Topologically inequivalent embeddings
    • 2
    • G.B. Mindlin H.G. Solari 1995 Topologically inequivalent embeddings Phys. Rev. E 52 2 1497 1502
    • (1995) Phys. Rev. e , vol.52 , pp. 1497-1502
    • Mindlin, G.B.1    Solari, H.G.2
  • 9
    • 22444455689 scopus 로고    scopus 로고
    • Topological analysis of chaotic dynamical systems
    • 4
    • R. Gilmore 1998 Topological analysis of chaotic dynamical systems Rev. Mod. Phys. 70 4 1455 1526
    • (1998) Rev. Mod. Phys. , vol.70 , pp. 1455-1526
    • Gilmore, R.1
  • 12
    • 15544370418 scopus 로고    scopus 로고
    • Fractional derivatives applied to phase space reconstructions
    • 1-4. Special Issue: Fractional Derivatives and Their Applications, O.P. Agrawal, J.A. Tenreiro Machado, and J. Sabatier (eds.)
    • B.F. Feeny G. Lin 2004 Fractional derivatives applied to phase space reconstructions Nonlinear Dyn. 38 1-4 85 99 Special Issue: Fractional Derivatives and Their Applications, O.P. Agrawal, J.A. Tenreiro Machado, and J. Sabatier (eds.)
    • (2004) Nonlinear Dyn. , vol.38 , pp. 85-99
    • Feeny, B.F.1    Lin, G.2
  • 13
    • 0026124343 scopus 로고
    • Fractional order state equations for the control of viscoelastically damped structures
    • 2
    • R.L. Bagley R.A. Calico 1991 Fractional order state equations for the control of viscoelastically damped structures AIAA J. Guid. 14 2 304 311
    • (1991) AIAA J. Guid. , vol.14 , pp. 304-311
    • Bagley, R.L.1    Calico, R.A.2
  • 14
    • 0032141482 scopus 로고    scopus 로고
    • Nonlinear vibrations of fractionally damped systems
    • 4
    • J. Padovan J.T. Sawicki 1998 Nonlinear vibrations of fractionally damped systems Nonlinear Dyn. 16 4 321 336
    • (1998) Nonlinear Dyn. , vol.16 , pp. 321-336
    • Padovan, J.1    Sawicki, J.T.2
  • 15
    • 0032154290 scopus 로고    scopus 로고
    • Numerical algorithm for dynamic problems involving fractional operators
    • 3
    • W. Zhang N. Shimizu 1998 Numerical algorithm for dynamic problems involving fractional operators JSME Int. J. Ser. C 41 3 364 370
    • (1998) JSME Int. J. Ser. C , vol.41 , pp. 364-370
    • Zhang, W.1    Shimizu, N.2
  • 16
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • J.H. He 1998 Approximate analytical solution for seepage flow with fractional derivatives in porous media Comput. Methods Appl. Mech. Eng. 167 57 68
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.167 , pp. 57-68
    • He, J.H.1
  • 17
    • 2842576194 scopus 로고    scopus 로고
    • A look at fractal functions through their fractional derivatives
    • 4
    • M. Stiassnie 1997 A look at fractal functions through their fractional derivatives Fractals 5 4 561 564
    • (1997) Fractals , vol.5 , pp. 561-564
    • Stiassnie, M.1
  • 18
    • 58149143583 scopus 로고    scopus 로고
    • Machado, J.A.T. (ed.) Special Issue of Fractional Order Calculs and its Applications
    • Machado, J.A.T. (ed.): Nonlinear Dyn. 29(1-4) (2002). Special Issue of Fractional Order Calculs and its Applications
    • (2002) Nonlinear Dyn. , vol.29 , Issue.1-4
  • 19
    • 15544372486 scopus 로고    scopus 로고
    • Fractional derivatives and their applications. Introduction
    • 1-4
    • O.P. Agrawal J.A.T. Machado J. Sabatier 2004 Fractional derivatives and their applications. Introduction Nonlinear Dyn. 38 1-4 1 2
    • (2004) Nonlinear Dyn. , vol.38 , pp. 1-2
    • Agrawal, O.P.1    MacHado, J.A.T.2    Sabatier, J.3
  • 21
    • 0033881047 scopus 로고    scopus 로고
    • Computation of fractional derivatives using fourier transform and digital FIR differentiator
    • C.-C. Tseng S.-C. Pei S.-C. Hsia 2000 Computation of fractional derivatives using fourier transform and digital FIR differentiator Signal Process. 80 151 159
    • (2000) Signal Process. , vol.80 , pp. 151-159
    • Tseng, C.-C.1    Pei, S.-C.2    Hsia, S.-C.3
  • 23
  • 27
    • 0032122999 scopus 로고    scopus 로고
    • Parametric identification of chaotic systems
    • 4
    • C.-M. Yuan B.F. Feeny 1998 Parametric identification of chaotic systems J. Vib. Control 4 4 405 426
    • (1998) J. Vib. Control , vol.4 , pp. 405-426
    • Yuan, C.-M.1    Feeny, B.F.2
  • 29
    • 4143093387 scopus 로고
    • Characterization of an experimental strange attractor by periodic orbits
    • D.P. Lathrop E.J. Kostelich 1989 Characterization of an experimental strange attractor by periodic orbits Phys. Rev. A 40 4028 4031
    • (1989) Phys. Rev. A , vol.40 , pp. 4028-4031
    • Lathrop, D.P.1    Kostelich, E.J.2
  • 30
    • 0013294485 scopus 로고
    • Unstable periodic orbits in the parametrically excited pendulum
    • 10
    • W. Van de Water M. Hoppenbrouwers F. Christiansen 1991 Unstable periodic orbits in the parametrically excited pendulum Phys. Rev. A 44 10 6388 6398
    • (1991) Phys. Rev. A , vol.44 , pp. 6388-6398
    • Van De Water, W.1    Hoppenbrouwers, M.2    Christiansen, F.3
  • 32
    • 0034257478 scopus 로고    scopus 로고
    • Fast multi-fractal analysis by recursive box covering
    • 9
    • B.F. Feeny 2000 Fast multi-fractal analysis by recursive box covering Int. J. Bifurc. Chaos 10 9 2277 2287
    • (2000) Int. J. Bifurc. Chaos , vol.10 , pp. 2277-2287
    • Feeny, B.F.1
  • 33
    • 0002221647 scopus 로고
    • Fast O(N) box-counting algorithm for estimating dimensions
    • 5
    • T.C.A. Molteno 1993 Fast O(N) box-counting algorithm for estimating dimensions Phys. Rev. E 48 5 R3263 R3266
    • (1993) Phys. Rev. e , vol.48
    • Molteno, T.C.A.1
  • 34
    • 33646981873 scopus 로고
    • Characterization of strange attractors
    • P. Grassberger I. Proccacia 1983 Characterization of strange attractors Phys. Rev. Lett. 50 346 349
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 346-349
    • Grassberger, P.1    Proccacia, I.2
  • 35
    • 0020850180 scopus 로고
    • Dimension of strange attractors: An experimental determination of the chaotic regime of two convective systems
    • G. Malraison P. Atten P. Berge M. Dubois 1983 Dimension of strange attractors: an experimental determination of the chaotic regime of two convective systems J. Phys. Lett. 44 897 902
    • (1983) J. Phys. Lett. , vol.44 , pp. 897-902
    • Malraison, G.1    Atten, P.2    Berge, P.3    Dubois, M.4
  • 37
    • 0003586464 scopus 로고
    • Plenum Press New York
    • Feder, J.: Fractals. Plenum Press, New York (1988)
    • (1988) Fractals
    • Feder, J.1
  • 38
    • 0000121132 scopus 로고
    • An experimentalist's introduction to the observation of dynamical systems
    • World Scientific Singapore
    • Gerschenfeld, N.: An experimentalist's introduction to the observation of dynamical systems. In: Hao, B.-L. (ed.) Directions in Chaos, vol. II. World Scientific, Singapore (1988)
    • (1988) Directions in Chaos , vol.2
    • Gerschenfeld, N.1    Hao, B.-L.2
  • 40
    • 0006697560 scopus 로고
    • Experimental observation of basins of attraction and homoclinic bifurcation in a magneto-mechanical oscillator
    • Wiley Chichester
    • Cusumano, J.P., Kimble, B.: Experimental observation of basins of attraction and homoclinic bifurcation in a magneto-mechanical oscillator. In: Thompson, J.M.T., Bishop, S.R. (eds.) Nonlinearity and Chaos in Engineering Dynamics, pp. 71-89. Wiley, Chichester (1994)
    • (1994) Nonlinearity and Chaos in Engineering Dynamics , pp. 71-89
    • Cusumano, J.P.1    Kimble, B.2    Thompson, J.M.T.3    Bishop, S.R.4
  • 41
    • 0001244839 scopus 로고
    • A stochastic intorrogation method for experimental measurements of global dynamics and basin evolution-application to a 2-well oscillator
    • 2
    • J.P. Cusumano B. Kimble 1994 A stochastic intorrogation method for experimental measurements of global dynamics and basin evolution-application to a 2-well oscillator Nonlinear Dyn. 8 2 213 235
    • (1994) Nonlinear Dyn. , vol.8 , pp. 213-235
    • Cusumano, J.P.1    Kimble, B.2
  • 42
    • 0035829652 scopus 로고    scopus 로고
    • Parametric identification of an experimental magneto-elastic oscillator
    • 5
    • B.F. Feeny C.M. Yuan J.P. Cusumano 2001 Parametric identification of an experimental magneto-elastic oscillator J. Sound Vib. 247 5 785 806
    • (2001) J. Sound Vib. , vol.247 , pp. 785-806
    • Feeny, B.F.1    Yuan, C.M.2    Cusumano, J.P.3
  • 43
    • 0031142828 scopus 로고    scopus 로고
    • Phase-space reconstructions and stick-slip
    • B.F. Feeny J.-W. Liang 1997 Phase-space reconstructions and stick-slip Nonlinear Dyn. 13 39 57
    • (1997) Nonlinear Dyn. , vol.13 , pp. 39-57
    • Feeny, B.F.1    Liang, J.-W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.