Peculiarities of Decomposition of Two-Timescale Models of Nonlinear Dynamic Systems

Abstract

The report is dedicated to the features of the dynamics of two-timescale dynamic systems and the problem of their models decomposition. A general model of nonlinear dynamic system represented by a system of differential equations in the Cauchy normal form is considered. In the process of model decomposition there is a need for a sequential solution of two problems: the determination of its belonging to a class of two-timescale models and the construction of a simplified model. For the case of a linear initial model, a procedure for solving both of these problems is proposed, which allows obtaining a simplified model of reduced order. In the case of a nonlinear initial model, there are no general methods for solving these problems. The conditions allowing one to reduce in principle the initial model in the Cauchy normal form to a singularly perturbed model with its subsequent decomposition are considered. However, the absence of strict theoretically based methods of such model transformation allows solving the problem only in some special cases. In the present report the authors discuss an approach of approximate solution of the decomposition problem of two-timescale model of the general form. The peculiarity of this approach is the representation of the decomposition result by a set of linear models at different time intervals of the processes implementation.