Choice of dynamical variables for global reconstruction of model equations from time series

Dmitry A. Smirnov, Boris P. Bezruchko, Yevgeny P. Seleznev
2002 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
The success of modeling from an experimental time series is determined to a significant extent by the choice of dynamical variables. We propose a method for preliminary investigation of a time series whose purpose is to find out whether a global dynamical model with smooth functions can be constructed for the chosen variables. The method consists in the estimation of single valuedness and continuity of relations between dynamical variables and variables to enter left-hand sides of model
more » ... s. The method is explained with numerical examples. Its efficiency is demonstrated by modeling a real nonlinear electric circuit. 1 Its length N and the dimension of its vectors are limited by the conditions of the experiment. 2 Coordinates of a vector x can be obtained by using the methods of successive derivatives ͓3,5,6͔, time delays ͓1,4,7-9͔, integration ͓6͔, or weighted summation ͓4͔. Besides, they may just coincide with the observables. The length of the series ͕x(t i )͖ can be less than N, but the difference is usually small. To avoid additional notations, we assume the length of ͕x(t i )͖ to be equal to N.
doi:10.1103/physreve.65.026205 pmid:11863630 fatcat:2rq5cge76zcpbd746gspssqwxa