메뉴 건너뛰기
Physical Review Letters
Volumn 68, Issue 4, 1992, Pages 427-430
Direct test for determinism in a time series
Author keywords

[No Author keywords available]
Indexed keywords

EID: 11944266815     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.68.427     Document Type: Article
Times cited : (324)
References (25)
  • 8
    • 84927397797 scopus 로고    scopus 로고
    • Parameters: r = 28, b = case 8 over 3, σ = 10.
  • 9
    • 0025039440 scopus 로고
    • The randomized time series are generated by randomizing the phases of the discrete Fourier transform of the original signal. The resulting signals are examples of Gaussian random processes equivalent to passing Gaussian random noise through a linear filter.
    • (1990) Circ. Res. , vol.67 , pp. 886
    • Kaplan, D.T.1    Cohen, R.J.2
  • 15
    • 84927397794 scopus 로고    scopus 로고
    • W. Feller, An Introduction to Probability Theory and Its Applications, Volume II (Wiley, New York, 1966). This result follows from the density function on p. 255 and is in accord with results in Refs. [8,9] for lower dimensions.
  • 16
    • 0001686163 scopus 로고
    • The Distribution of Distance in a Hypersphere
    • Computations not shown give R bar2d= 2d-2Γ ( d / 2 ) Γ (d / 2 ) / π1/2Γ ( d- 1/2 ). This equals 2 / pi, 2/3, 32/15 pi for d = 2,3,4, respectively. R bar2d approaches 1 / sqrt 2 for d -> inf in accord with earlier calculations:
    • (1950) The Annals of Mathematical Statistics , vol.21 , pp. 447
    • Hammersley, J.M.1
  • 21
    • 84927397793 scopus 로고    scopus 로고
    • Feller, Ref. [11], pp. 80–87.
  • 22
    • 84927397792 scopus 로고    scopus 로고
    • The dependence of Λ bar on tau is more complex in other situations. For example, dynamical systems such as the Rossler system or a lightly damped harmonic oscillator have PSI (T) that oscillate with an envelope that falls off only slowly to zero. Random signals with such PSI (T) show L barnd->&Rmacrnd when PSI ( τ ) -> 0 and when tau is near a maximum or minimum of PSI (T), particularly for small epsilon.
  • 25
    • 84927397791 scopus 로고    scopus 로고
    • All calculations reported here were performed on a SUN SparcStation IPC with 8 Mb RAM. Details on the sorting algorithms that enable analysis of high-dimensional systems will be presented elsewhere. A typical run with a time series of 250000 points and 220 boxes takes app 100 CPU seconds.

* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.