Modeling chaotic evolution with nonlinear Langevin dynamics

In order to statistically describe chaotic time series numerically or exper imentally observed, we propose a new approach to statistically model the ob served data. This is carried out by first introducing temporally coarse-gra ined quantities. Then we derive a set of nonlinear Langevin equations of mo tion for these quantities by employing the projection-operator method devel oped in nonequilibrium statistical mechanics to treat systems near thermal equilibrium. This set of equations simulates the observed time series. We a pply the present approach to a time series generated by the Rossler model o f chaos. Comparing power spectra from Langevin equations of motion with tho se from the Rossler model, we find that the modeled Langevin dynamics simul ates the original observed time series quite well.