ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


Threshold stability of the synchronous mode in a power grid with hub cluster topology

The main purpose of this paper is to investigate the dynamics of the power grid model with hub cluster topology based on the Kuramoto equations with inertia. It is essential to study the stability of synchronous grid operation mode and to find conditions of its global stability. The conditions that ensure establishment of the synchronous mode instead of coexisting asynchronous ones are considered. Methods. In this paper we use numerical modelling of different grid operation modes.

Frequency entrainment and anti-entrainment of coupled active rotators synchronized by common noise

Topic and Aim. We study the effect of common noise on the ensemble of coupled active rotators. Such a noise always has a synchronizing effect on the system, whereas the coupling may be attracting (synchronizing) or repulsing

Frequency repulsion in ensembles of general limit-cycle oscillators synchronized by common noise in the presence of global desynchronizing coupling

Topic. We study the interaction of two fundamentally different synchronization mechanisms: by means of coupling and by means of the driving by a random signal, which is identical for all oscillators – common noise. Special attention is focused on the effect of frequency divergence arising from the competition between these mechanisms. Aim. The aim of the paper is to construct a universal theory describing such an interaction for a general class of smooth limit-cycle oscillators with a global coupling.

Synchronization and multi-frequency quasi-periodicity in the dynamics of coupled oscillators

The dynamics of ensembles of oscillators containing a small number of bibitemlits is discussed. The possible types of regimes and pecularities of bifurcations of regular and quasi-periodic attractors are analyzed. By using the method of Lyapunov exponents charts the picture of  embedding of quasi-periodic regimes of different dimension in the parameter space is revealed. Dynamics of ensembles of van der Pol and phase oscillators are compared.

External synchronization of traveling waves in an active medium in self-sustained and excitable regime

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.

Multistability in dynamical small world networks

  We explore phase multistability which takes place in an ensemble of periodic oscillators under the action of long-distance couplings, which appear randomly between the arbitrary cells. The  system under study is Kuromoto’s model with additional dynamical interconnections between phase oscillators. The sequence of bifurcations, which accompany increasing of the strength of the global coupling is determined. Regions of multistability existance are defined.

Phenomenon of the van der pol equation

  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.

Investigating nonlinear granger causality method efficiency at strong synchronization of systems

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.

The study of multistability and external synchronization in nonautonomous system of two coupled van der pol oscillators with repulsive coupling

  In this paper we study the bifurcational mechanisms of synchronization and multistability formation in a system of two interacting van der Pol oscillators, one of which is under external harmonic forcing. We draw a two­parametric bifurcation diagram for phasereduced system and study its evolution in transition from symmetrical to asymmetrical repulsive interaction. Relying on the results of bifurcation analysis of non­reduced system we conclude that the synchronization scenarios found in the phase­reduced system correspond to the ones in the non­reduced system.

A new information transfer scheme based on phase modulation of a carrier chaotic signal

  A new information transfer scheme based on dynamical chaos is suggested. An analog carrier signal is generated by self­exciting chaotic generator in a phase­coherent oscillatory regime. This carrier undergoes a modified procedure of phase modulation by information signal, which simultaneously affects upon the transmitting generator via the feedback loop. After the communication channel is passed, the signal modulated by information acts upon a receiving generator, so that a synchronous chaotic response arises in it.