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