Reconstruction of equations

Time-delayed systems, including coupled ones, became popular models of different physical and biological objects. Often One or few variables of such models cannot be directly measured, these variables are called hidden variables. However, reconstruction of models from experimental signals in presence of hidden variables can be very suitable for model verification and indirect measurement.

Purpose. To suggest a new approach to reconstruction of couping architecture and individual parameters of first-order time-delayed oscillators from experimental series of their oscillations.

The methods for the reconstruction of model delay-differential equations for ensembles of coupled time-delay systems from their time series are proposed. The methods efficiency is illustrated using chaotic and periodic time series from chains of diffusively coupled model and experimental time-delay systems for the cases of unidirectional andmutual coupling.

The methods are proposed for the reconstruction of time-delay systems modeled by neutral  delay-differential equations from their time series. The methods are successfully applied to the recovery of generalized Mackey–Glass equation and equations modeling ship rolling and human movement from simulated data.