synchronization

In present paper the phenomena of coherence resonance, mutual and external synchronization of noise-induced stochastic oscillations in FitzHugh–Nagumo system are studied by means of numerical and natural experiments. The properties of attractor in the system as well as energy exchange processes are analyzed. Self-sustained character of stochastic oscillations in non-autonomous FitzHugh–Nagumo system justified.

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.

We investigate dynamical states formed in a network of coupled phase oscillators in which strength of interactions between oscillators evolve dynamically depending on their relative phases.

The article is devoted to Robert Adler, the man who combined activities as theoretical physicist, an experimental physicist and engineer-inventor, the owner of more than 200 patents. Brief biographical information about this remarkable man is presented, and a more detailed presentation of the results of his two famous studies is given, known as Adler’s gated-beam tube and Adler’s equation.

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.

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.

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 75the 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 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 2N¡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.

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.