16 research outputs found
Stochastic to deterministic crossover of fractal dimension for a Langevin equation
Using algorithms of Higuchi and of Grassberger and Procaccia, we study
numerically how fractal dimensions cross over from finite-dimensional Brownian
noise at short time scales to finite values of deterministic chaos at longer
time scales for data generated from a Langevin equation that has a strange
attractor in the limit of zero noise. Our results suggest that the crossover
occurs at such short time scales that there is little chance of
finite-dimensional Brownian noise being incorrectly identified as deterministic
chaos.Comment: 12 pages including 3 figures, RevTex and epsf. To appear Phys. Rev.
E, April, 199
Is there a climatic attractor ?
Much of our information on climatic evolution during the past million years comes from the time series describing the isotope record of deep-sea cores. A major task of climatology is to identify, from this apparently limited amount of information, the essential features of climate viewed as a dynamic system. Using the theory of nonlinear dynamic systems we show how certain key properties of climate can be determined solely from time series data. © 1984 Nature Publishing Group.SCOPUS: ar.jinfo:eu-repo/semantics/publishe