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


Bifurcation analysis of synchronization and amplitude death in coupled generators with inertial nonlinearity

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 non-identical excitement parameters the first-type synchronization regions merge together.

Synchronization in coupled self­sustained oscillators with non­-identical parameters

The particular properties of dynamics are discussed for dissipatively coupled van der Pol oscillators, non-identical in values of parameters controlling the Andronov–Hopf bifurcation and nonlinear dissipation. Possibility of a special synchronization regime in an infinitively long band between oscillator death and quasiperiodic areas is shown for such system. Non-identity of parameters of nonlinear dissipation results in specific form of the boundary of the main synchronization tongue, which looks like the mirror letter S.

Intermittency of type­-I with noise and eyelet intermittency

In this article we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency) supposed hitherto to be the different phenomena. We prove that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is proven by the consideration of different sample systems, such as quadratic map, van der Pol oscillator and Rossler system.

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.

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.

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.

On the way towards multidimensional tori

The problem of the dynamics of three coupled self-oscillators and three coupled periodically driven self-oscillators 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 four-frequency tori and chaos are revealed. Three typical situations of synchronization of three self-oscillators by the external driving are found. First situation refers to the mode locking of autonomous oscillators.

Synchronizing the period-­2 cycle in the system of symmetrical coupled populations with stock–recruitment based on the Ricker population model

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.

Experimental study of type I intermittency in a generator synchronized with external harmonic signal in the presence of noise

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. 

Technique of investigation of synchronization between oscillatory processes with the frequency of 0.1 Hz in the human cardiovascular system

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.