Method of timedelay systems recovery from time series with known type of model equation

We propose the method for the reconstruction of firstorder timedelay systems from their time series. The method is based on taking into account the type of the system equation at the regression model construction. The method allows one to recover the delay time, the parameter characterizing the inertial properties of the system and the nonlinear function. It can be applied to the recovery of timedelay systems performing chaotic and periodic oscillations.