Stochastic modelling of intermittency.
Recently, methods have been developed to model low-dimensional chaotic systems in terms of stochastic differential equations. We tested such methods in an electronic circuit experiment. We aimed to obtain reliable drift and diffusion coefficients even without a pronounced time-scale separation of the chaotic dynamics. By comparing the analytical solutions of the corresponding Fokker-Planck equation with experimental data, we show here that crisis-induced intermittency can be described in terms of a stochastic model which is dominated by state-space-dependent diffusion. Further on, we demonstrate and discuss some limits of these modelling approaches using numerical simulations. This enables us to state a criterion that can be used to decide whether a stochastic model will capture the essential features of a given time series.
Stemler
Thomas
T
School of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley 6009, WA, Australia. thomas@maths.uwa.edu.au
Werner
Johannes P
JP
Benner
Hartmut
H
Just
Wolfram
W