синхронизация.

Detecting the direction of coupling between systems using records of their oscillations is an actual task for many areas of knowledge. Its solution can hardly be achieved in case of synchronization. Granger causality method is promising for this task, since it allows to hope for success in the case of partial (e.g., phase) synchronization due to considering not only phases but also amplitudes of both signals. In this paper using the etalon test systems with pronounced time scale the method

This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radio­engineering, physics and mathematics. The review outlines only one essential point of his work, associated with the equation that bears his  name, and has a surprisingly wide range of applications in natural sciences. In this review we discuss the following matters.

• The biography of van der Pol, history of his equation and supposed precursors.

• The contribution of A.A. Andronov in the theory of self­oscillations.

The model of a one-dimensional active medium, which cell represents FitzHugh–Nagumo oscillator, is studied with periodical boundary conditions. Such medium can be either self-oscillatory or excitable one in dependence of the parameters values. Periodical boundary conditions provide the existence of traveling wave regimes both in excitable anself-oscillatory case without any deterministic or stochastic impacts.

Based on the analysis of experimental data we study the collective dynamics of ensembles from several tens nephrons located on a kidney surface. Using wavelet­analysis, the phenomenon of locking of instantaneous frequencies and phases is studied that is caused by the tubulo­glomerular feedback. It is shown that structural units of the kidney related to distinct nephron trees participate in clusters formation. The entrainment of frequencies and phases of oscillations for large groups of nephrons occurs only for some fragments of experimental data.

In this article Wilson-Cowan model for interactions of excitatory and inhibitory neurons and model of currency oscillations on a Forex market were considered.

Switching activity in the ensemble of inhibitory coupled Poicare systems is considered. The existence of heteroclinic contour in the phase space at the certain domain of parameter space has shown.

Dynamics of the ensemble of non-identical inhibitory and diffusively coupled systems of Poincare is considered. The approximate bifurcation diagrams for all qualitatively different regimes of the network activity have shown. There are areas of the parameter space corresponding to different dynamic regimes, such as multistability, extinction, modulation, bursting and synchronization.