синхронизация

We study synchronization in ensembles of locally diffusive coupled Bonhoeffer–van der Pol oscillators. Individual elements frequencies influence on excitation propagation in one- and two-dimensional media is investigated. We show that excitation propagation speed depends on frequency mismatch between synchronization frequency and elements’ individual frequencies. Qualitative and quantitative results describing this effect are numerical modeling data and analytical research.

The dynamics of the four dissipatively coupled van der Pol oscillator is considered. Lyapunov chart is presented in the parameter plane and its arrangement is discusses. The effect of increase of the threshold for the «oscillator death» regime and the possibility of complete and partial broadband synchronization are revealed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators, in particular, quasi-periodic saddle-node and Hopf bifurcations.

We explore the destruction of phase multistability which takes place in an ensemble of period doubling oscillators under the action of long-distance couplings, which appear randomly between the arbitrary cells. The investigation is carried out on the example of a chain of Rossler’s oscillators with periodic boundary conditions, where alongside with local couplings between the elements exist long-range interconnections. The sequence of bifurcations, which accompany increasing of the strength of the global coupling is determined.

A numerical simulation of a wide band or secure communication scheme, based on nonlinear admixture of an information signal to the chaotic one, and on synchronization of the transmitter and receiver generators, manifesting hyperbolic chaos. Synchronization of the transmitter and receiver is provided by a strong unidirectional coupling between them. The study of the possibility of synchronization between subsystems and functionality of the communication scheme are presented.

The problem of the excitation of two coupled oscillators is discussed in the case of the simple subharmonic resonance between the external force and eigen-frequencies of the oscillators. The corresponded phase equation is obtained.