системы с запаздыванием

The features of collective dynamics of oscillators are studied in an ensemble of identical bistable time-delay systems globally coupled via the mean field. The influence of inertial properties and delay of the mean field on the collective dynamics of oscillators is considered. It is shown that a variety of oscillation regimes in the ensemble is caused by the presence of bistable states with considerably different basic frequencies in coupled oscillators.

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.

The method is proposed for delay time estimation in time-delay systems from their time series. The method is based on the nearest neighbor method. It can be applied to a wide class of time-delay systems and it is still efficient under very high levels of dynamical and measurement noise.

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.