synchronization

We study synchronization in one- and two-dimentional ensembles of nonidentical Bonhoeffer–van der Pol oscillators. Small chains (number of elements N 6 4) are proved to have not less than 2N¡1 coexisting stable different synchronous regimes. The chain of N elements is supposed to have not less than 2N¡1 synchronous regimes at the same values of parameters. Formation of synchronization clusters at weak coupling is shown. Regimes, provided by existing of waves, setting rhythm for all elements in ensemble, are investigated.

We study synchronization of two coupled nonidentical Bonhoeffer–van der Pol oscillators. Coexistence of two different synchronous regimes is proved. Mechanisms of synchronous regimes origination and destruction are investigated. Fluctuations influence on syncronous regimes is considered. It is found that noise can cause: i) synchronization destruction and beating originations; ii) fluctuations-caused bistability destruction; iii) fluc-tuations-caused intermittency of synchronous regimes without synchronization destruction.

Аn experimental study of statistical properties of type I intermittency in the presence of noise is presented. For the first time an electronic experiment to study periodic oscillations synchronization destruction in case of small detuning in the presence of noise is held. The results are found to be in accordance with theory.

Synchronization between the processes of vegetative regulation of the heart rate and blood pressure in the vessels of microcirculatory channel having in humans a fundamental frequency of about 0.1 Hz is studied. A method for quantitative estimation of the degree of synchronization between these processes is proposed. The method is based on the calculation of a summary percent of phase synchronization of oscillations. A statistical significance of the calculated coefficient of synchronization is analyzed.

Different universal methods of calculation of index of chaotic synchronization are considered. One of the methods, which is based on mutual coherence function, is presented in more detail. Its advantages and disadvantages, sensibility to external noise and distortions are discussed. Application of the algorithm to process of destruction of complete chaotic synchronization in two coupled systems with discrete time are demonstrated.

The problem of the dynamics of three coupled self­oscillators and three coupled periodically driven self­oscillators is discussed, in the last case only one of the oscillators is directly exited by the external fore. The regions of complete synchronization, two­, three­and four­frequency tori and chaos are revealed. Three typical situations of synchronization of three self­oscillators by the external driving are found.

We investigated coupled map lattices based on the Ricker model that describes the spatial dynamics of heterogeneous populations represented by two connected groups of individuals with a migration interaction between them. Bifurcation mechanisms in­phase and antiphase synchronization of multistability regimes were considered in such systems. To identify a synchronization mode we introduced the quantitative measure of synchronization.

Synchronization phenomena are studied in phase dynamics approximation in the periodically driven system of two coupled oscillators. The cases are discussed when the autonomous oscillators demonstrate phase locking or beats with incommensurate frequencies. Lyapunov charts are presented, the possible regimes of dynamics of the driven system are discussed. Different types of two­dimensional tori are revealed and classified.

This paper deals with the influence of the passive elements on the synchronization in the ensembles of coupled non­identical Bonhoeffer–van der Pol oscillators. With a help of numerical experiment it was demonstrated that the introduction of passive elements may lead to both increase and decrease of global synchronization threshold in the system. These results were confirmed analytically using piecewise linear approximation of the Bonhoeffer–van der Pol model.

The results of analysis of bifurcation transitions to synchronous regimes and amplitude death are discussed for two dissipatively coupled generators with inertial nonlinearity. It was determined that there are two types of synchronization regions in this system: first consists of both frequency lock and suppression areas, second has only frequency lock area. At the weakly non­identical excitement parameters the first­type synchronization regions merge together.