Danish Ph.D. School in Nonlinear Science

Sponsored by the Danish Research Academy

What can global reconstruction accomplish ?

by Natalia Janson
Saratov State University
Nonlinear Dynamics Laboratory
410026, Astrakhanskaya str. 83

MIDIT-seminar 399

Tuesday January 27, 1998, 15.00 h
at MIDIT, IMM Building 305, room 027

Abstract: Black boxes and time series. General ideas and aims of GR. Creation of dynamical systems in the form of ODE's or a map reproducing the initial realization with the required accuracy - and "nothing more". What does it mean in fact: one obtains a dynamical description of the regime which reproduces the original evolution operator approximation, valid in a small vicinity of the regime under study. The use of transient process time series to check if the form of approximate evolution operator (dimension and right-hand parts) is chosen properly, since the transient trajectories depend on the dimensions and shape of different manifolds including separatrix surfaces.

Areas of application.

Reconstruction of the phase space partition into trajectories in the close vicinity of the regime under study being more reliable than in case when only the time series is analysed.
Sometimes, a relatively short time series is necessary to obtain a dynamical description while it is impossible to evaluate reliably statistical and dynamical characteristics on the data available. If we succeed in GR, then we are able to evaluate everything with the reqired accuracy.
Modeling of stationaty regimes from the time series produced by a system with slowly varying parameters, i.e., from nonstationary data.
Exploiting GR for multichannel communication.