Geodesic
Reconstruction of coupling architecture and parameters of time-delayed oscillators in ensembles from time series
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 24 (2016) no. 3, pp. 21-37.

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Purpose. To suggesta new approach to reconstruction of couping architecture and individual parameters of first-order time-delayed oscillators from experimental series of their oscillations. Method. The method is based on minimization of target function, which characterizes a distance between points of nonlinear function of a current oscillator, whichis to be reconstructed. Then estimated coupling coefficients are split into significant and insignificant. Minimization of target function is processed with least squares routine. Delay time is estimated as a trial delay corresponding to a minimum of target function over all trial delays. Results. Efficiency of the proposed method was demonstrated in numerical experiment from time series of an ensemble of diffusively coupled non identical Mackey-Glass oscillators in presence of noise. Also a hardware experiment was considered in which resistively coupled generators with delay line were studied. The method demonstrated higher computational efficiency than previously suggested approaches due to use of not iterative algorithms for target function minimization and significant coefficient selection. Herewith estimates of coupling coefficients and inertance parameter are asymptotically unbiased. Discussion. The proposed approach may be useful for reconstruction of parameters of elements and coupling architecture in systems of different nature: radioengineering, biological or others, which can be described using first-order time-delay equations.
Keywords: Time-series analyses, reconstruction of equations, ensembles of oscillators, time-delayed systems. 
@article{IVP_2016_24_3_a2,
     author = {I. V. Sysoev and D. D. Kulminskij and V. I. Ponomarenko and M. D. Prokhorov},
     title = {Reconstruction of coupling architecture and parameters of time-delayed oscillators in ensembles from time series},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {21--37},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2016_24_3_a2/}
}
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I. V. Sysoev; D. D. Kulminskij; V. I. Ponomarenko; M. D. Prokhorov. Reconstruction of coupling architecture and parameters of time-delayed oscillators in ensembles from time series. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 24 (2016) no. 3, pp. 21-37. http://geodesic.mathdoc.fr/item/IVP_2016_24_3_a2/