메뉴 건너뛰기




Volumn 12, Issue 3, 2002, Pages 549-558

Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0036710131     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1487570     Document Type: Article
Times cited : (100)

References (23)
  • 2
    • 34249988665 scopus 로고
    • Extracting qualitative dynamics from experimental data
    • D.S. Broomhead and G.P. King, "Extracting qualitative dynamics from experimental data," Physica D 20, 217-236 (1986).
    • (1986) Physica D , vol.20 , pp. 217-236
    • Broomhead, D.S.1    King, G.P.2
  • 3
    • 44049117992 scopus 로고
    • An analytic approach to practical state space reconstruction
    • J.F. Gibson, J.D. Farmer, M. Casdagli, and S. Eubank, "An analytic approach to practical state space reconstruction," Physica D 57, 1-30 (1992).
    • (1992) Physica D , vol.57 , pp. 1-30
    • Gibson, J.F.1    Farmer, J.D.2    Casdagli, M.3    Eubank, S.4
  • 5
    • 0042075109 scopus 로고
    • Retrieving dynamical invariants from chaotic data using NARMAX models
    • L.A. Aguirre and S.A. Billings, "Retrieving dynamical invariants from chaotic data using NARMAX models," Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, 449-474 (1994).
    • (1994) Int. J. Bifurcation Chaos Appl. Sci. Eng. , vol.5 , pp. 449-474
    • Aguirre, L.A.1    Billings, S.A.2
  • 7
    • 34250315551 scopus 로고
    • Continuous control of chaos by self-controlling feedback
    • K. Pyragas, "Continuous control of chaos by self-controlling feedback," Phys. Lett. A 170, 421-428 (1990).
    • (1990) Phys. Lett. A , vol.170 , pp. 421-428
    • Pyragas, K.1
  • 8
    • 0343689904 scopus 로고
    • Synchronization in chaotic systems
    • L.M. Pecora and T.L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 821-824
    • Pecora, L.M.1    Carroll, T.L.2
  • 9
    • 0029251476 scopus 로고
    • Controllability and observability of linear systems: Some noninvariant aspects
    • L.A. Aguirre, "Controllability and observability of linear systems: Some noninvariant aspects," IEEE Trans. Educ. 38, 33-39 (1995).
    • (1995) IEEE Trans. Educ. , vol.38 , pp. 33-39
    • Aguirre, L.A.1
  • 10
    • 0032475780 scopus 로고    scopus 로고
    • On the nonequivalence of observables in phase space reconstructions from recorded time series
    • C. Letellier, J. Maquet, L. Le Sceller, G. Gouesbet, and L.A. Aguirre, "On the nonequivalence of observables in phase space reconstructions from recorded time series," J. Phys. A 31, 7913-7927 (1998).
    • (1998) J. Phys. A , vol.31 , pp. 7913-7927
    • Letellier, C.1    Maquet, J.2    Le Sceller, L.3    Gouesbet, G.4    Aguirre, L.A.5
  • 11
    • 4243234987 scopus 로고    scopus 로고
    • Structure selection for global vector field reconstruction by using the identification of fixed points
    • L. Le Sceller, C. Letellier, and G. Gouesbet, "Structure selection for global vector field reconstruction by using the identification of fixed points," Phys. Rev. E 60, 1600-1606 (1999).
    • (1999) Phys. Rev. E , vol.60 , pp. 1600-1606
    • Le Sceller, L.1    Letellier, C.2    Gouesbet, G.3
  • 12
    • 0001600637 scopus 로고
    • Construction of phenomenological models from numerical scalar time series
    • G. Gouesbet and J. Maquet, "Construction of phenomenological models from numerical scalar time series," Physica D 58, 202-215 (1992).
    • (1992) Physica D , vol.58 , pp. 202-215
    • Gouesbet, G.1    Maquet, J.2
  • 13
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • O.E. Rössler, "An equation for continuous chaos," Phys. Lett. A 57, 397-398 (1976).
    • (1976) Phys. Lett. A , vol.57 , pp. 397-398
    • Rössler, O.E.1
  • 14
    • 0000531057 scopus 로고    scopus 로고
    • Use of synchronization and adaptive control in parameter estimation from a time series
    • A. Maybhate and R.E. Amritkar, "Use of synchronization and adaptive control in parameter estimation from a time series," Phys. Rev. E 59, 284-293 (1999).
    • (1999) Phys. Rev. E , vol.59 , pp. 284-293
    • Maybhate, A.1    Amritkar, R.E.2
  • 15
    • 0001576305 scopus 로고
    • Local false nearest neighbors and dynamical dimensions from observed chaotic data
    • H.D.I. Abarbanel and M.B. Kennel, "Local false nearest neighbors and dynamical dimensions from observed chaotic data," Phys. Rev. E 47, 3057-3068 (1993).
    • (1993) Phys. Rev. E , vol.47 , pp. 3057-3068
    • Abarbanel, H.D.I.1    Kennel, M.B.2
  • 16
    • 0001874436 scopus 로고    scopus 로고
    • Practical method for determining the minimum embedding dimension of a scalar time series
    • L. Cao, "Practical method for determining the minimum embedding dimension of a scalar time series," Physica D 110, 43-52 (1997).
    • (1997) Physica D , vol.110 , pp. 43-52
    • Cao, L.1
  • 17
    • 0003792312 scopus 로고
    • Prentice-Hall, Englewood Cliffs
    • T. Kailath, Linear Systems (Prentice-Hall, Englewood Cliffs, 1980).
    • (1980) Linear Systems
    • Kailath, T.1
  • 18
    • 85000250825 scopus 로고
    • Deterministic nonperiodic flow
    • E.N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141 (1963).
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 19
    • 0030291304 scopus 로고    scopus 로고
    • Topological characterization of reconstructed attractors modding out symmetries
    • C. Letellier and G. Gouesbet, "Topological characterization of reconstructed attractors modding out symmetries," J. Phys. II 6, 1615-1638 (1996).
    • (1996) J. Phys. II , vol.6 , pp. 1615-1638
    • Letellier, C.1    Gouesbet, G.2
  • 20
    • 18644373835 scopus 로고    scopus 로고
    • Covering dynamical systems: Twofold covers
    • C. Letellier and R. Gilmore, "Covering dynamical systems: Twofold covers," Phys. Rev. E 63, 016206 (2001).
    • (2001) Phys. Rev. E , vol.63 , pp. 016206
    • Letellier, C.1    Gilmore, R.2
  • 21
    • 0001240065 scopus 로고
    • The proto-lorenz system
    • R. Miranda and E. Stone, "The proto-Lorenz system," Phys. Lett. A 178, 105-113 (1993).
    • (1993) Phys. Lett. A , vol.178 , pp. 105-113
    • Miranda, R.1    Stone, E.2
  • 22
    • 0021785427 scopus 로고
    • Influence of detuning on the properties of laser equations
    • H. Zeghlache and P. Mandel, "Influence of detuning on the properties of laser equations," J. Opt. Soc. Am. B 2, 18-22 (1985).
    • (1985) J. Opt. Soc. Am. B , vol.2 , pp. 18-22
    • Zeghlache, H.1    Mandel, P.2
  • 23
    • 84958272946 scopus 로고    scopus 로고
    • Modding out a continuous rotation symmetry for disentangling a laser dynamics
    • in press
    • C. Letellier, "Modding out a continuous rotation symmetry for disentangling a laser dynamics," Appl. Sci. Eng. (in press).
    • Appl. Sci. Eng.
    • Letellier, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.