Reconstruction of self-oscillating systems with delay time modulation

The aim of our research is to study the possibility of reconstruction from time series the self-oscillating systems with variable time delay, demonstrating regimes of turbulent and laminar chaos. Methods. The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. The possibility of estimating the parameters of systems with delay time modulation from their time series is considered using the known method for reconstructing systems with constant delay time, which is based on statistical analysis of time intervals between all possible pairs of extrema in time series. A new method for estimating the parameters of systems with variable delay time is proposed, based on statistical analysis of time intervals between two successive extrema in time series. Results. It is shown that in some cases the known methods for reconstructing systems with constant delay time are also effective for reconstructing systems with varying delay time. With their help, one can estimate the mean delay time and recove the nonlinear function of the system. The proposed method, aimed at application to time-delay systems with delay time modulation, allows one to estimate the frequency and amplitude of delay time modulation. Conclusion. The obtained results are of interest to various scientific disciplines that study systems with variable delay times based on their time series.