Open AccessChaotic characteristic interperted by 250 step chaometry and its applying to the heart rate
Author(s) -
Luo Chuan-Wen
Publication year - 2007
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.56.6282
Subject(s) - orbit (dynamics) , attractor , chaotic , lorenz system , mathematics , series (stratigraphy) , mathematical analysis , convergence (economics) , fixed point , rate of convergence , computer science , paleontology , channel (broadcasting) , computer network , artificial intelligence , economic growth , engineering , economics , biology , aerospace engineering
A discrete orbit is seperated into m pieces, eaoh constituted of k near points. The monopolized sphere capacity of a point is the extent seperating this one from the others. Instantaneous chaometry, which represents the total capacity of the k monopolized spheres, showes the total seperating extent of a orbital piece.The k step chaometry is the mean of the instantaneous chaometries of the m orbital pieces. The convergent property of k step chaometry is proved for the asymptotic periodic orbit. Althongh the convergence of k step chaometry has not been proved mathematically for the chaotic orbit, it is verified by numerical analysis. Lorenz attractor is interpreted by the 250 step chaometry. The powerful interpreting capability is shown by the 250 step chaometry of 3_dimensional and x component of the Lorenz system. The regression equation between the 250 step chaometry and the age of the 71 normal sinus heart rate time series is y=6.4623 -0.0496x with the correlation coefficient r=-0.669, which supports the view point of Goldberger, and means that the 250 step chaometry will decrease to zero before 130 years of age.