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A method for separating laminar and turbulent phases in coupled systems occurring near the boundary of generalized chaotic synchronization is proposed that is based on calculations of local Lyapunov exponents. The suitability of the proposed method has been verified in relation to systems with unidirectional coupling, which admit the analysis of intermittency with the aid of an auxiliary system approach. Results obtained by the two methods are compared to show good mutual agreement.

The phenomenon of generalized synchronization onset between mutually coupled beam-plasma systems (Pierce diodes) with supercritical currents has been discovered. It is established that the appearance of a synchronous regime is related to the change in one Lyapunov exponent from a positive to negative value. The results of the analysis are confirmed by the nearest-neighbor method.

The propagation of pulses in a model chain of Hindmarsh-Rose neurons with unidirectional coupling has been studied in the presence of intrinsic dynamics in chain elements. The main regimes of oscillations in the model chain are determined as dependent on the coupling parameter. The mechanisms of activation and suppression of oscillations in the model chain under the action of rectangular pulses are explained using the results of a detailed analysis of the basins of attraction of a stable immobile point and a periodic attractor of a model neuron.

The results of a numerical investigation of the behavior of two model self-excited oscillators with vacuum microtriodes coupled with one another by a unidirectional coupling are presented. It is shown that the behavior of such self-excited oscillators (each of which, being a system with one degree of freedom, can exhibit only periodic oscillations) is quite complicated: Not only periodic and quasiperiodic but also chaotic oscillations are possible in the system. A state diagram is constructed in the plane of the controlling parameters frequency detuning — magnitude of the coupling.