Reconstruction of time-delayed feedback systems from time series

2005 ◽  
Vol 203 (3-4) ◽  
pp. 209-223 ◽  
Author(s):  
M.D. Prokhorov ◽  
V.I. Ponomarenko ◽  
A.S. Karavaev ◽  
B.P. Bezruchko
Keyword(s):  
Time Series ◽  
Delayed Feedback ◽  
Feedback Systems ◽  
Time Delayed Feedback

scholarly journals Identification of Couplings in Adaptive Dynamical Networks of Time-Delayed Feedback Oscillators

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2200
Author(s):  
Ilya V. Sysoev ◽  
Danil D. Kulminskiy ◽  
Vladimir I. Ponomarenko ◽  
Mikhail D. Prokhorov
Keyword(s):  
Time Series ◽  
A Priori ◽  
Linear Optimization ◽  
Target Function ◽  
Delayed Feedback ◽  
Connectivity Matrix ◽  
Nonlinear Functions ◽  
Estimated Parameters ◽  
Unbiased Estimates ◽  
Time Delayed Feedback

An approach to solve the inverse problem of the reconstruction of the network of time-delay oscillators from their time series is proposed and studied in the case of the nonstationary connectivity matrix. Adaptive couplings have not been considered yet for this particular reconstruction problem. The problem of coupling identification is reduced to linear optimization of a specially constructed target function. This function is introduced taking into account the continuity of the nonlinear functions of oscillators and does not exploit the mean squared difference between the model and observed time series. The proposed approach allows us to minimize the number of estimated parameters and gives asymptotically unbiased estimates for a large class of nonlinear functions. The approach efficiency is demonstrated for the network composed of time-delayed feedback oscillators with a random architecture of constant and adaptive couplings in the absence of a priori knowledge about the connectivity structure and its evolution. The proposed technique extends the application area of the considered class of methods.

Identifying noise sources of time-delayed feedback systems

2004 ◽  
Vol 328 (2-3) ◽  
pp. 219-224 ◽  
Author(s):  
T.D Frank ◽  
P.J Beek ◽  
R Friedrich
Keyword(s):  
Delayed Feedback ◽  
Feedback Systems ◽  
Noise Sources ◽  
Time Delayed Feedback

REAL-TIME ANTICIPATION OF CHAOTIC STATES OF AN ELECTRONIC CIRCUIT

2002 ◽  
Vol 12 (07) ◽  
pp. 1619-1625 ◽  
Author(s):  
HENNING U. VOSS
Keyword(s):  
Real Time ◽  
Electronic Circuit ◽  
Delayed Feedback ◽  
Feedback Systems ◽  
Experimental Realization ◽  
Driving Circuit ◽  
Time Delayed Feedback

This Letter presents an experimental realization of a recently proposed method to anticipate future states of nonlinear time-delayed feedback systems. The electronic circuit allows for a real-time anticipation of even strongly irregular signals. It is found that synchronization of the driven circuit with chaotic future states of the driving circuit is insensitive to signal and system perturbations.

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