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


Controll of multistability by means of bi­phase resonance force

We propose a new method of control of phase multistability in two coupled selfsustained oscillators. The method is based on the «pulling» of phases of oscillations to the target mode under two external harmonic forces, which influence the first and the second sub-systems simultaneosly. Varying the phase shift between the external signals results in control of switching between coexisting oscillating modes. Effectiveness of the method is demonstrated on the example of switching between periodic and chaotic regimes in two Chua’s oscillatotrs.

Synchronization of oscillations in the dynamics of ensembles of surface nephrons

Based on the analysis of experimental data we study the collective dynamics of ensembles from several tens nephrons located on a kidney surface. Using wavelet-analysis, the phenomenon of locking of instantaneous frequencies and phases is studied that is caused by the tubulo-glomerular 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.

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.

On quasi-­synchronous regimes in a phase lock loop with the second­-order filter and approximate inclusion of the delay

For a typical phase lock loop with the second-order filter and delayed feedback, conditions of appearance and characteristics of regular and chaotic automodulation regimes are studied.

Synchronization of the system of two competing modes by external harmonic signal

Forced synchronization of self-oscillating system with two degrees of freedom is studied in the case when there are no resonance relations between eigenfrequencies and interaction of the modes has the form of mode competition. Stability conditions for the regimes of one- and two-frequency oscillations are obtained analytically. The structure of synchronization tongues on the frequency–amplitude of external driving parameters plane is studied numerically.

Effect of external periodic force on the dynamics of thecharge domains in semiconductor superlattice

Periodic external signal effect on the collective dynamics of charge in semiconductor superlattice is studied. It is shown, that periodically-oscillating external electrical field can synchronize the transport of domains of the high density of charge as well as oscillations of electrical current flowing through the superlattice.

Modeling of cardiac activity on the basis of maps: ensembles of coupled elements

The dynamics of coupled maps’ ensembles is investigated in the context of description of spatio-temporal processes in the myocardium. Particular, the dynamics of two coupled maps is explored as well as modeling the interaction of pacemaker (oscillatory) cell and myocyte (excitable cell), and the interation of two pacemakers. Setting of synchronous regime by increasing of coupling strength is considered through a coincidence of their characteristic time scales (characteristic frequencies).

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.

Phase dynamics of periodically driven quasiperiodic self­-vibrating oscillators

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 two-dimensional tori are revealed and classified.

Influence of passive elements on the synchronization of oscillatory ensembles

This paper deals with the influence of the passive elements on the synchronization in the ensembles of coupled non-identical 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.