INVERTING CHAOS - EXTRACTING SYSTEM PARAMETERS FROM EXPERIMENTAL-DATA

Given a set of experimental or numerical chaotic data and a set of mod el differential equations with several parameters, is it possible to d etermine the numerical values for these parameters using a least-squar es approach, and thereby to test the model against the data? We explor e this question (a) with simulated data from model equations for the R ossler, Lorenz, and pendulum attractors, and (b) with experimental dat a produced by a physical chaotic pendulum. For the systems considered in this paper, the least-squares approach provides values of model par ameters that agree well with values obtained in other ways, even in th e presence of modest amounts of added noise. For experimental data, th e ''fitted'' and experimental attractors are found to have the same co rrelation dimension and the same positive Lyapunov exponent. (C) 1996 American Institute of Physics.