synchronization

The particular properties of dynamics are discussed for dissipatively coupled van der Pol oscillators, non­identical 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. Non­identity of parameters of nonlinear dissipation results in specific form of the boundary of the main synchronization tongue, which looks like the mirror letter S.

In this article we compare the characteristics of two types of the intermittent behavior (type­I 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 R ̈ossler system.

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. In this paper using the etalon test systems with pronounced time scale the method

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.

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.

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

Forced synchronization of self­oscillating 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 two­frequency oscillations are obtained analytically. The structure of synchronization tongues on the frequency–amplitude of external driving parameters plane is studied numerically. Mechanisms of establishing of the synchronous regime are considered depending on coefficients of non­linear mode coupling.

The dynamics of coupled maps’ ensembles is investigated in the context of description of spatio­temporal 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.

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 the ensemble consisting of three phase­locked 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 quasi­synchronous regimes are distinguished in the parameter space; the restructuring of the dynamics behavior on the boards of the distinguished districts is analyzed.