synchronization

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 sub­systems 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.

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 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.

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.

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.

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.

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 R ¨ossler systems and circle map.

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, two-parametric bifurcation diagrams and phase portraits. Possible types of motion in driven system are discussed.

We study synchronization in ensembles of locally diffusive coupled Bonhoeffer–van der Pol oscillators. Individual elements frequencies influence on excitation propagation in one- and two-dimensional media is investigated. We show that excitation propagation speed depends on frequency mismatch between synchronization frequency and elements’ individual frequencies. Qualitative and quantitative results describing this effect are numerical modeling data and analytical research.

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, quasi-periodic saddle-node and Hopf bifurcations.