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


Methods of measuring chaotic synchronization

Different universal methods of calculation of index of chaotic synchronization are considered. One of the methods, which is based on mutual coherence function, is presented in more detail. Its advantages and disadvantages, sensibility to external noise and distortions are discussed. Application of the algorithm to process of destruction of complete chaotic synchronization in two coupled systems with discrete time are demonstrated.

Variety of synchronous regimes in ensembles of nonidentical oscillators: Chain and lattice

We study synchronization in one- and two-dimentional ensembles of nonidentical Bonhoeffer–van der Pol oscillators. Small chains (number of elements N <= 4) are proved to have not less than 2 N−1 coexisting stable different synchronous regimes. The chain of N elements is supposed to have not less than 2 N−1 synchronous regimes at the same values of parameters. Formation of synchronization clusters at weak coupling is shown. Regimes, provided by existing of waves, setting rhythm for all elements in ensemble, are investigated.

Variety of synchronous regimes in ensembles of nonidentical oscillators: two coupled elements

We study synchronization of two coupled nonidentical Bonhoeffer–van der Pol oscillators. Coexistence of two different synchronous regimes is proved. Mechanisms of synchronous regimes origination and destruction are investigated. Fluctuations influence on syncronous regimes is considered. It is found that noise can cause: i) synchronization destruction and beating originations; ii) fluctuations-caused bistability destruction; iii) fluctuations-caused intermittency of synchronous regimes without synchronization destruction.

Mixing and diffusion effect on spatial-temporal dynamics in stochastic Lotka–Volterra system with discrete phase space

The influence of two types of diffusion on dynamics of stochastic lattice Lotka– Volterra model is considered in this work. The simulations were carried out by means of Kinetic Monte-Carlo algorithm. It is shown that the local diffusion considerably changes the dynamics of the model and accelerates the interaction processes on the lattice, while the mixing results in appearance of global periodic oscillations. The global oscillations appear due to phenomenon of phase synchronization.

Synchronization waves in weak-nonlinear oscillatory ensembles

Synchronization is studied in ensembles of locally dissipative coupled and conservative coupled weak-nonlinear van der Pol oscillators. In the chain of N elements not less than 2 N−1 different regimes of global synchronization are stable at the same values of parameters. Cluster synchronization is considered as well. Existing of multiple fronts of synchronization switching is shown. These fronts go one through another without of changing or reflections from free boundaries.

Synchronization of periodic oscillation in a delayed-feedback oscillator by external harmonic driving

Dynamics of a delayed-feedback oscillator with cubic nonlinearity driven by an external harmonic signal is considered in a case when in the free-running oscillator periodic regime is realized. Resonance curves, i.e. amplitude–frequency responses of the oscillator are derived analytically. Stability conditions for synchronization regime are analyzed. Synchronization tongues on the driving amplitude – driving frequency parameter plane are presented. General differences from classical picture of synchronization of the systems with one degree of freedom are discussed.

A new information transfer scheme based on phase modulation of a carrier chaotic signal

A new information transfer scheme based on dynamical chaos is suggested. An analog carrier signal is generated by self­exciting chaotic generator in a phase­coherent oscillatory regime. This carrier undergoes a modified procedure of phase modulation by information signal, which simultaneously affects upon the transmitting generator via the feedback loop. After the communication channel is passed, the signal modulated by information acts upon a receiving generator, so that a synchronous chaotic response arises in it.

The study of multistability and external synchronization in nonautonomous system of two coupled van der pol oscillators with repulsive coupling

In this paper we study the bifurcational mechanisms of synchronization and multistability formation in a system of two interacting van der Pol oscillators, one of which is under external harmonic forcing. We draw a two­parametric bifurcation diagram for phasereduced system and study its evolution in transition from symmetrical to asymmetrical repulsive interaction. Relying on the results of bifurcation analysis of non­reduced system we conclude that the synchronization scenarios found in the phase­reduced system correspond to the ones in the non­reduced system.

Dynamics of two field­coupled spin­transfer oscillators

The model of two field­coupled spin­transfer oscillators has been derived and studied. It has been shown that this model demonstrates phase synchronization in a wide bandwidth, quasiperiodic oscillations and chaos.

Coupled self-­sustained oscillators of different nature by example of van der Pol system and brusselator

Problem of interaction between self­sustained oscillating systems of different nature is discussed by an example of coupled brusselator and van der Pol oscillator. Picture of leading oscillator changing with the growth of coupling parameter is shown. Areas of different types of dynamics are indicated in the parameter space. The case of essentially different eigenfrequencies is discussed.