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Volumn 55, Issue 5, 1997, Pages 5398-5417

Extracting unstable periodic orbits from chaotic time series data

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EID: 4243769823     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.5398     Document Type: Article
Times cited : (112)

References (40)
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    • ibid. P Cvitanović, Phys. Rev. Lett. 61, 2729 (1988);
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    • [Nature 365, 411 (1993)] and E. Ott and M. L. Spano [Phys. Today 48(5), 34 (1995)].
    • (1993) Nature , vol.365 , pp. 411
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  • 16
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    • used an experimentally determined periodic orbit to analyze a crisis in their system [Phys. Lett. A 153, 105 (1991)].
    • (1989) Phys. Rev. A , vol.40 , pp. 4028
  • 17
    • 0000576711 scopus 로고
    • Recently D. Pierson and F. Moss [Phys. Rev. Lett. 75, 2124 (1995)] and X. Pei and F. Moss [Nature 379, 619 (1996)] have introduced a method for locating fixed points in data. This method is based on recurrence together with criteria derived from the local behavior near a fixed point.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 2124
  • 21
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    • It has recently come to our attention that a similar approach to fixed point detection was considered by J. N. Glover in his Ph.D. dissertation (Statistical Laboratory, D.P.M.M.S., The University of Cambridge)
    • It has recently come to our attention that a similar approach to fixed point detection was considered by J. N. Glover in his Ph.D. dissertation (Statistical Laboratory, D.P.M.M.S., The University of Cambridge).
  • 24
    • 85037217063 scopus 로고    scopus 로고
    • For continuous time systems, a discrete representation of the dynamics can be obtained by a Poincaré surface of section. In the case when the dynamics is driven by a periodic signal, a stroboscopic surface of section can also be applied by sampling the continuous time signal at every period of the drive
    • For continuous time systems, a discrete representation of the dynamics can be obtained by a Poincaré surface of section. In the case when the dynamics is driven by a periodic signal, a stroboscopic surface of section can also be applied by sampling the continuous time signal at every period of the drive.
  • 25
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    • Springer-Verlag, Berlin
    • F. Takens, in Dynamical Systems and Turbulence, edited by D. Rand and L. S. Young (Springer-Verlag, Berlin, 1981), p. 230.
    • (1981) Dynamical Systems and Turbulence , pp. 230
    • Takens, F.1
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    • E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993), p. 87
    • E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993), p. 87.
  • 29
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    • There could be other points a 0 mapping to z-|Ax(0z-|Ax(a). (The mapping Gzz-|Ax need not be invertible.) In this case, D-|(Formula presented)(z-|Ax(0)) is min((Formula presented)(0),(Formula presented)(a
    • There could be other points a≠0 mapping to z-|Ax(0)=z-|Ax(a). (The mapping G:z→z-|Ax need not be invertible.) In this case, D-|(Formula presented)(z-|Ax(0)) is min((Formula presented)(0),(Formula presented)(a)).
  • 30
    • 85037224821 scopus 로고    scopus 로고
    • Qz) is degenerate only in the special case where the two roots of det((Formula presented)-λ(Formula presented))=0 are the same, where (Formula presented) is the two by two matrix (Formula presented) and (Formula presented) is the two by two matrix (Formula presented), i, j=1,2
    • Q(z) is degenerate only in the special case where the two roots of det((Formula presented)-λ(Formula presented))=0 are the same, where (Formula presented) is the two by two matrix (Formula presented) and (Formula presented) is the two by two matrix (Formula presented), i, j=1,2.
  • 31
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    • An example of these fixed points can be found in systems near a crisis (see J. C. Sommerer et al. in Ref. 5)
    • An example of these fixed points can be found in systems near a crisis (see J. C. Sommerer et al. in Ref. 5).
  • 34
    • 85037230514 scopus 로고    scopus 로고
    • Ref. 11, the Gaussian scaled phase shuffle is called the amplitude adjusted Fourier transform (see Ref. 11 for a detailed description of its construction procedure)
    • In Ref. 11, the Gaussian scaled phase shuffle is called the amplitude adjusted Fourier transform (see Ref. 11 for a detailed description of its construction procedure).
  • 37
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    • With the same reasoning, in systems with slowly varying parameters, using temporal neighbors to estimate the values of ∇ F for the Taylor expansion might be more appropriate than using spatial neighbors. In all the examples in Sec. V, we used temporal neighbors
    • With the same reasoning, in systems with slowly varying parameters, using temporal neighbors to estimate the values of ∇F for the Taylor expansion might be more appropriate than using spatial neighbors. In all the examples in Sec. V, we used temporal neighbors.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.