Structural acceleration method in the estimation of parameters from a time series in Chen chaotic system

An adaptive control method and a structural acceleration method are introduced for estimating the unknown parameter when a time series for a scalar function of the variables of a nonlinear dynamical model is given. The methods are shown to work when the scalar function explicitly depends on a variable with the evolution equation in which the parameter appears explicitly, and the structural acceleration method is shown to work should the previously adaptive control method not work. The structural acceleration method provides a solution to extract the parameter out from a time series for the scalar function of the variables of chaotic systems. Numerical simulations are presented for Chen chaotic system.