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


«Oscillator death» and quasiperiodic bifurcations in low-dimensional ensemble of van der Pol oscillators

The dynamics of the four dissipatively coupled van der Pol oscillator is considered. Lyapunov chart is presented in the parameter plane and its arrangement is discusses. The effect of increase of the threshold for the «oscillator death» regime and the possibility of complete and partial broadband synchronization are revealed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators, in particular, quasiperiodic saddle-node and Hopf bifurcations.

Calcium oscillations in astrocytes. Part 2 Dynamics of interacting calcium oscillators

We investigated bifurcation mechanisms of oscillatory dynamics of interacting chemically excitable cells (astrocytes). In model of three interacting astrocytes we studied bifurcation transitions leading to generation of calcium oscillations induced by the intercellular diffusion. We analyzed basic mechanisms of limit cycle instabilities and destructions, typical transitions to chaotic oscillations and basic properties of intercellular synchronization.

Calcium oscillations in astrocytes. Part 1 Astrocyte as generator of calcium oscillations

Bifurcation mechanisms of oscillatory dynamics in a biophysical model of chemically excitable brain cells (astrocytes) were analyzed. In contrast to neuronal oscillators widely studied in nonlinear dynamics the astrocytes do not possess electrical excitability but capable to generate chemical oscillations which modulate neuronal signaling. Astrocyte dynamics is described by third-order system of ordinary differential equations derived from biophysical kinetics.

Coherent resonance in klystron oscillators on self-excitation threshold

This work presents experimental results of synchronization of coherent resonance phenomena in cascade klystron oscillator with delayed feedback on self-excitation threshold. Degree of coherence, signal-to-noise ratio and synchronization wideband for single and cascade klystron oscillators were compared.

Spectral components’ behavior in coupled pierce diodes near the phase synchronization boundary

In this article we study the dynamics of two unidirectionally coupled Pierce diodes near the phase synchronization boundary in terms of synchronization of spectral components. We show that systems under consideration demonstrate self-similar behavior with any value of coupling strength within the region of our study. The results correlate with the data of the similar research for Rossler systems and circle map. 

Synchronization of reactively coupled phase oscillators driven by external force

Synchronization of two reactively coupled van der Pol oscillators with external force is investigated in this paper. We consider and compare quasi-periodic motion of oscillators with frequency-locked mode. The paper includes maps of Lyapunov’s exponents, twoparametric bifurcation diagrams and phase portraits. Possible types of motion in driven system are discussed.

On modelling the dynamics of coupled self-oscillators using the simplest phase maps

The problem of describing the dynamics of coupled self-oscillators using discrete time systems on the torus is considered. We discuss the methodology for constructing such maps as a simple formal models, as well as physically motivated systems. We discuss the differences between the cases of the dissipative and inertial coupling. Using the method of Lyapunov exponents charts we identify the areas of two- and three-frequency quasiperiodicity and chaos. Arrangement of the Arnold resonance web is investigated and compared for different model systems. 

Control of multistability and forced synchronization in coupled self-sustained oscillators with period-doubling bifurcations

Control of phase multistability and synchronization are investigated in two coupled Feigenbaum systems on example of Chua’s generators, coupled through symmetric diffusive link. The control is fulfilled by externel periodic signals, which simultaneously influence the both oscillators with equal amplitudes and frequencies, but with different phases. The behaviour of the system is explored in depandence on amplitude, frequency and phase difference between the signals. Influence of the phase difference on width of the synchronization tongue is considered.

Dynamics of three coupled van der Pol oscillators with non-identical controlling parameters

We consider the chain of three dissipatively coupled self-oscillating systems with non-identical controlling parameters. We observe situations, when coupling damps different oscillators. The structure of the frequency mismatch – coupling value parameter plane is investigated with a view to the location of oscillator death area, complete synchronization area, two- and three-frequency quasiperiodic regimes. Features, connected with non-identity in controlling parameters, are considered.

Nonlinear dynamics of a ring of three phase systems

Nonlinear dynamics of the ensemble consisting of three phase-locked generators, which are coupled in a ring, is discovered. By force of computational modeling, which is based on the theory of oscillations, the regimes of the generators collective behavior is examined; the districts of synchronous and quasi-synchronous regimes are distinguished in the parameter space; the restructuring of the dynamics behavior on the boards of the distinguished districts is analyzed.