generalized synchronization

A method is proposed for generalized synchronization detection which does not exploit an auxiliary system. The method operates in a real time and uses a single response system that is driven alternately by the drive system signal and its delayed copy. A system of secure communication based on the proposed method is developed that has high resistance to noises of a transmission channel.

The behavior of the Pierce diode has been considered from the point of view of the spatial Lyapunov exponents. The method of calculation of the spectrum of the spatial Lyapunov exponents for the electron spatial extended systems has been proposed. The autonomous dynamics of the Pierce diode as well as the behavior of two unidirectionally coupled Pierce diodes when the generalized synchronization is taken place have been considered.

Effect of noise on generalized synchronization in spatially extended systems described by Ginzburg–Landau equations being in the spatio-temporal chaotic regime is studied. It is shown, that noise does not affect the synchronous regime threshold in such systems. The reasons of the revealed particularity have been explained by means of the modified system approach and confirmed by the results of numerical simulation.

The behavior of the boundary of generalized synchronization in two unidirectionally coupled chaotic oscillators depending on the value of the control parameter mismatch between interacting systems has been studied. Peculiarities in its behavior in the field of the relatively large values of the control parameter mistuning have been found. The character of this behavior and physical mechanisms resulting in the generalized synchronization regime onset in such systems have been explained by the analysis of the spectral compound of signal from response system.