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Volumn 61, Issue 6, 2000, Pages 6485-6489

Detecting unstable periodic orbits from transient chaotic time series

Author keywords

[No Author keywords available]

Indexed keywords

TIME SERIES; VECTOR SPACES; ACOUSTIC NOISE; ALGORITHMS; GRAPH THEORY; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PROBABILITY;

EID: 0034205556     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.6485     Document Type: Article
Times cited : (36)

References (44)
  • 3
    • 85036376209 scopus 로고    scopus 로고
    • T. Tél, in Directions in Chaos, edited by Bai-lin Hao (World Scientific, Singapore, 1990) Vol.3
    • T. Tél, in Directions in Chaos, edited by Bai-lin Hao (World Scientific, Singapore, 1990) Vol.3
  • 4
    • 0004210476 scopus 로고    scopus 로고
    • Bai-lin Hao, World Scientific, Singapore
    • in STATPHYS 19, edited by Bai-lin Hao (World Scientific, Singapore, 1996).
    • (1996) STATPHYS 19
  • 5
    • 0003915006 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, England, and references therein
    • Analyzing chaotic time series is such a rich field that even a partial list of the relevant papers is impossible here. See, for example, H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, England, 1997), and references therein.
    • (1997) Nonlinear Time Series Analysis
    • Kantz, H.1    Schreiber, T.2
  • 6
    • 0001085819 scopus 로고
    • We are only aware of the following paper on analyzing transient chaotic time series which focuses on the reconstruction of the vector space by using embedding: I.M. Jánosi and T. Tél, Phys. Rev. E 49, 2756 (1994).
    • (1994) Phys. Rev. E , vol.49 , pp. 2756
    • Jánosi, I.M.1    Tél, T.2
  • 7
    • 85036388597 scopus 로고    scopus 로고
    • Chaos Focus Issue 3 (4) (1993)
    • Chaos Focus Issue 3 (4) (1993).
  • 20
    • 0000878650 scopus 로고
    • P. Cvitanović, Focus Issue on Periodic Orbit Theory, Chaos 2, (1992)
    • Phys. Rev. AD. Auerbach, 41, 6692 (1990);P. Cvitanović, Focus Issue on Periodic Orbit Theory, Chaos 2, (1992)
    • (1990) Phys. Rev. A , vol.41 , pp. 6692
    • Auerbach, D.1
  • 22
    • 29444438680 scopus 로고
    • M. Dhamala and Y.-C. Lai (unpublished)
    • C. Grebogi, E. Ott, and J.A. Yorke, Phys. Rev. A 37, 1711 (1988);M. Dhamala and Y.-C. Lai (unpublished).
    • (1988) Phys. Rev. A , vol.37 , pp. 1711
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 24
    • 0001024141 scopus 로고
    • Detection of unstable periodic orbits embedded in chaotic attractors has been an active area of investigation. For additional work besides Ref. 12, see, for example, G.B. Mindlin, X.-J. Hou, H.G. Solari, R. Gilmore, and N.B. Tufillaro, Phys. Rev. Lett. 64, 2350 (1990)
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 2350
    • Mindlin, G.B.1    Hou, X.-J.2    Solari, H.G.3    Gilmore, R.4    Tufillaro, N.B.5
  • 34
    • 0003513785 scopus 로고
    • D. Rand, L. S. Young, Springer-Verlag, Berlin
    • F. Takens, in Dynamical Systems and Turbulence, edited by D. Rand and L. S. Young, Lecture Notes in Mathematics Vol. 898 (Springer-Verlag, Berlin, 1981), p. 366
    • (1981) Dynamical Systems and Turbulence , pp. 366
    • Takens, F.1
  • 37
    • 0000390258 scopus 로고    scopus 로고
    • The definition of the probability studied in that paper was, however, slightly different from the one considered in the present paper
    • The corresponding problem for chaotic attractors was discussed in X. Pei, K. Dolan, F. Moss, and Y.-C. Lai, Chaos 8, 853 (1998). The definition of the probability studied in that paper was, however, slightly different from the one considered in the present paper.
    • (1998) Chaos , vol.8 , pp. 853
    • Pei, X.1    Dolan, K.2    Moss, F.3    Lai, Y.-C.4
  • 44
    • 0002870373 scopus 로고
    • Briefly, the method is as follows. Take a line segment intersecting the stable manifold in a region containing the chaotic saddle. Divide the line segment into a large number of subintervals and compute (Formula presented) the number of subintervals whose lifetimes under the inverse dynamics are larger than or equal to n, where the lifetime is the time within which a trajectory remains in the region. It was suggested that (Formula presented) scales with n as (Formula presented), where (Formula presented) is the topological entropy of the chaotic saddle [Q. Chen, E. Ott, and L.P. Hurd, Phys. Lett. A 156, 48 (1991)].
    • (1991) Phys. Lett. A , vol.156 , pp. 48
    • Chen, Q.1    Ott, E.2    Hurd, L.P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.