메뉴 건너뛰기




Volumn 38, Issue 1-4, 2004, Pages 85-99

Fractional derivatives applied to phase-space reconstructions

Author keywords

Chaos; Embeddings; Fractional derivatives; Phase space reconstructions

Indexed keywords

CHAOS THEORY; FOURIER TRANSFORMS; FUNCTIONS; SAMPLING; TOPOLOGY; VECTORS;

EID: 15544370418     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-004-3748-6     Document Type: Conference Paper
Times cited : (14)

References (41)
  • 1
    • 35949006791 scopus 로고
    • Determining embedding dimension for phase-space reconstruction using a geometrical construction
    • Kennel, M., Brown, R., and Abarbanel, H. D. I., 'Determining embedding dimension for phase-space reconstruction using a geometrical construction', Physical Review A 45, 1992, 3403-3411.
    • (1992) Physical Review A , vol.45 , pp. 3403-3411
    • Kennel, M.1    Brown, R.2    Abarbanel, H.D.I.3
  • 3
    • 0000779360 scopus 로고
    • Detecting strange attractors in turbulence
    • Takens, F., 'Detecting strange attractors in turbulence', Lecture Notes in Mathematics 898, 1981, 366-381.
    • (1981) Lecture Notes in Mathematics , vol.898 , pp. 366-381
    • Takens, F.1
  • 6
    • 0001628622 scopus 로고
    • Reconstructing attractors from scalar time series: A comparison of singular system analysis and redundancy criteria
    • Fraser, A. M., 'Reconstructing attractors from scalar time series: A comparison of singular system analysis and redundancy criteria', Physica D 34, 1989, 391-404.
    • (1989) Physica D , vol.34 , pp. 391-404
    • Fraser, A.M.1
  • 7
    • 0033531045 scopus 로고    scopus 로고
    • Comments on the physical interpretation of proper orthogonal modes in vibrations
    • Ravindra, B., 'Comments on the physical interpretation of proper orthogonal modes in vibrations', Journal of Sound and Vibration 219(1), 1999, 189-192.
    • (1999) Journal of Sound and Vibration , vol.219 , Issue.1 , pp. 189-192
    • Ravindra, B.1
  • 8
    • 34548696055 scopus 로고
    • Independent coordinates for strange attractors from mutual information
    • Fraser, A. M. and Swinney, H. L., 'Independent coordinates for strange attractors from mutual information', Physical Review A 33(2), 1986, 1134-1140.
    • (1986) Physical Review A , vol.33 , Issue.2 , pp. 1134-1140
    • Fraser, A.M.1    Swinney, H.L.2
  • 9
    • 0001874436 scopus 로고    scopus 로고
    • Practical method for determining the minimum embedding dimension of a scalar time series
    • Cao, L., 'Practical method for determining the minimum embedding dimension of a scalar time series', Physica D 110, 1997, 43-50.
    • (1997) Physica D , vol.110 , pp. 43-50
    • Cao, L.1
  • 10
    • 0001762008 scopus 로고    scopus 로고
    • Distortions of reconstruction for chaotic attractors
    • Potopov, A., 'Distortions of reconstruction for chaotic attractors', Physica D 101, 1997, 207-226.
    • (1997) Physica D , vol.101 , pp. 207-226
    • Potopov, A.1
  • 11
    • 0042020821 scopus 로고
    • Topologically inequivalent embeddings
    • Mindlin, G. B. and Solari, H. G., 'Topologically inequivalent embeddings', Physical Review E 52(2), 1995, 1497-1502.
    • (1995) Physical Review E , vol.52 , Issue.2 , pp. 1497-1502
    • Mindlin, G.B.1    Solari, H.G.2
  • 12
    • 0031142828 scopus 로고    scopus 로고
    • Phase-space reconstructions and stick-slip
    • Feeny, B. F. and Liang, J. W., 'Phase-space reconstructions and stick-slip', Nonlinear Dynamics 13(1), 1997, 39-57.
    • (1997) Nonlinear Dynamics , vol.13 , Issue.1 , pp. 39-57
    • Feeny, B.F.1    Liang, J.W.2
  • 13
    • 22444455689 scopus 로고    scopus 로고
    • Topological analysis of chaotic dynamical systems
    • Gilmore, R., 'Topological analysis of chaotic dynamical systems', Review of Modern Physics 70(4), 1998, 1455-1526.
    • (1998) Review of Modern Physics , vol.70 , Issue.4 , pp. 1455-1526
    • Gilmore, R.1
  • 17
    • 4143093387 scopus 로고
    • Characterization of an experimental strange attractor by periodic orbits
    • Lathrop, D. P. and Kostelich, E. J., 'Characterization of an experimental strange attractor by periodic orbits', Physical Review A 40, 1989, 4028.
    • (1989) Physical Review A , vol.40 , pp. 4028
    • Lathrop, D.P.1    Kostelich, E.J.2
  • 19
    • 29444438680 scopus 로고
    • Unstable periodic orbits and the dimensions of multifractal chaotic attractors
    • Grebogi, C., Ott, E., and Yorke, J., 'Unstable periodic orbits and the dimensions of multifractal chaotic attractors', Physical Review A 37(5), 1988, 1711-1724.
    • (1988) Physical Review A , vol.37 , Issue.5 , pp. 1711-1724
    • Grebogi, C.1    Ott, E.2    Yorke, J.3
  • 20
    • 0001380235 scopus 로고
    • Characterization and detection of parameter variations of nonlinear mechanical systems
    • Kesaraju, R. V. and Noah, S. T., 'Characterization and detection of parameter variations of nonlinear mechanical systems', Nonlinear Dynamics 6, 1994, 433-457.
    • (1994) Nonlinear Dynamics , vol.6 , pp. 433-457
    • Kesaraju, R.V.1    Noah, S.T.2
  • 22
    • 0032122999 scopus 로고    scopus 로고
    • Parametric identification of chaotic systems
    • Yuan, C.-M. and Feeny, B. F., 'Parametric identification of chaotic systems', Journal of Vibration and Control 4(4), 1998, 405-426.
    • (1998) Journal of Vibration and Control , vol.4 , Issue.4 , pp. 405-426
    • Yuan, C.-M.1    Feeny, B.F.2
  • 23
    • 0035829652 scopus 로고    scopus 로고
    • Parametric identification of an experimental two-well oscillator
    • Feeny, B. F., Yuan, C.-M., and Cusumano, J. P., 'Parametric identification of an experimental two-well oscillator', Journal of Sound and Vibration 247(5), 2001, 785-806.
    • (2001) Journal of Sound and Vibration , vol.247 , Issue.5 , pp. 785-806
    • Feeny, B.F.1    Yuan, C.-M.2    Cusumano, J.P.3
  • 24
    • 0000121132 scopus 로고
    • An Experimentalist's introduction to the observation of dynamical systems
    • Hao Bai-Lin (ed.), World Scientific, Singapore
    • Gerschenfeld, N., 'An Experimentalist's introduction to the observation of dynamical systems', in Directions in Chaos, Vol. II, Hao Bai-Lin (ed.), World Scientific, Singapore, 1988.
    • (1988) Directions in Chaos , vol.2
    • Gerschenfeld, N.1
  • 25
    • 0003586464 scopus 로고
    • Plenum Press, New York
    • Feder, J., Fractals, Plenum Press, New York, 1988.
    • (1988) Fractals
    • Feder, J.1
  • 26
    • 0034257478 scopus 로고    scopus 로고
    • Fast multifractal analysis by recursive box-covering
    • Feeny, B. F., 'Fast multifractal analysis by recursive box-covering', International Journal of Bifurcations and Chaos 10(9), 2000, 2277-2287.
    • (2000) International Journal of Bifurcations and Chaos , vol.10 , Issue.9 , pp. 2277-2287
    • Feeny, B.F.1
  • 28
    • 0020850180 scopus 로고
    • Dimension of strange attractors: An experimental determination of the chaotic regime of two convective systems
    • Malraison, G., Atten, P., Berge, P., and Dubois, M., 'Dimension of strange attractors: An experimental determination of the chaotic regime of two convective systems', Journal of Physics Letters 44, 1983, 897-902.
    • (1983) Journal of Physics Letters , vol.44 , pp. 897-902
    • Malraison, G.1    Atten, P.2    Berge, P.3    Dubois, M.4
  • 30
    • 0026124343 scopus 로고
    • Fractional order state equations for the control of viscoelastically damped structures
    • Bagley, R. L. and Calico, R. A., 'Fractional order state equations for the control of viscoelastically damped structures', AIAA Journal of Guidance 14(2), 1991, 304-311.
    • (1991) AIAA Journal of Guidance , vol.14 , Issue.2 , pp. 304-311
    • Bagley, R.L.1    Calico, R.A.2
  • 31
    • 0032141482 scopus 로고    scopus 로고
    • Nonlinear vibrations of fractionally damped systems
    • Padovan, J. and Sawicki, J. T., 'Nonlinear vibrations of fractionally damped systems', Nonlinear Dynamics 16(4), 1998, 321-336.
    • (1998) Nonlinear Dynamics , vol.16 , Issue.4 , pp. 321-336
    • Padovan, J.1    Sawicki, J.T.2
  • 32
    • 0032154290 scopus 로고    scopus 로고
    • Numerical algorithm for dynamic problems involving fractional operators
    • Zhang, W. and Shimizu, N., 'Numerical algorithm for dynamic problems involving fractional operators', JSME International Journal, Series C 41(3), 1998, 364-370.
    • (1998) JSME International Journal, Series C , vol.41 , Issue.3 , pp. 364-370
    • Zhang, W.1    Shimizu, N.2
  • 33
    • 0032307661 scopus 로고    scopus 로고
    • Approximate analytical solution for seepage flow with fractional derivatives in porous media
    • He, J. H., 'Approximate analytical solution for seepage flow with fractional derivatives in porous media', Computational Methods in Applied Mechanics and Engineering 167, 1998, 57-68.
    • (1998) Computational Methods in Applied Mechanics and Engineering , vol.167 , pp. 57-68
    • He, J.H.1
  • 34
    • 2842576194 scopus 로고    scopus 로고
    • A look at fractal functions through their fractional derivatives
    • Stiassnie, M., 'A look at fractal functions through their fractional derivatives', Fractals 5(4), 1997, 561-564.
    • (1997) Fractals , vol.5 , Issue.4 , pp. 561-564
    • Stiassnie, M.1
  • 37
    • 30244493399 scopus 로고    scopus 로고
    • Long memory processes and fractional integration in econometrics
    • Baillie, R. T., 'Long memory processes and fractional integration in econometrics', Journal of Econometrics 73(1), 1996, 5-59.
    • (1996) Journal of Econometrics , vol.73 , Issue.1 , pp. 5-59
    • Baillie, R.T.1
  • 38
    • 0033881047 scopus 로고    scopus 로고
    • Computation of fractional derivatives using Fourier transform and digital FIR differentiator
    • Tseng, C.-C., Pei, S.-C., and Hsia, S.-C., 'Computation of fractional derivatives using Fourier transform and digital FIR differentiator', Signal Processing 80, 2000, 151-159.
    • (2000) Signal Processing , vol.80 , pp. 151-159
    • Tseng, C.-C.1    Pei, S.-C.2    Hsia, S.-C.3
  • 41


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.