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Schiff, S.1
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used an experimentally determined periodic orbit to analyze a crisis in their system [Phys. Lett. A 153, 105 (1991)].
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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.
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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)
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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).
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24
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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
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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.
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25
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0003513785
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Springer-Verlag, Berlin
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F. Takens, in Dynamical Systems and Turbulence, edited by D. Rand and L. S. Young (Springer-Verlag, Berlin, 1981), p. 230.
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Takens, F.1
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E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993), p. 87
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E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993), p. 87.
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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
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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)).
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30
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85037224821
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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
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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.
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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)
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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).
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34
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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)
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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).
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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
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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.
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40
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0027980735
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S. J. Schiff, K. Jerger, T. Chang, T. Sauer and P. G. Aitken, Biophys. J. 67, 684 (1994).
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Schiff, S.J.1
Jerger, K.2
Chang, T.3
Sauer, T.4
Aitken, P.G.5
|