synchronization

Topic. The paper is devoted to the study of mutual synchronization of two gyrotrons coupled with delay. As a rule, a theoretical study of synchronization of gyrotrons and other microwave oscillators is usually carried out by numerical simulations using certain well-established models of microwave electronics. Using this approach, it is difficult to provide a fairly complete synchronization pattern, using methods and ideas of nonlinear dynamics.

Subject of the study. Recently, the problems of synchronization of systems demonstrating

Aim. The aim of the paper is to study the mutual synchronization of two periodic self- sustained oscillators with a detuning of frequencies interacting through a memristor. It is supposed to give an answer to the question of the possibility of synchronization in this case and of its probable features. Method.

The work is devoted to study of multistability of traveling waves in a ring of harmonic oscillators with a linear non-local couplings. It analyses the influence of the strength and radius of the couplings on stability of spatially periodic regimes with different values of their wavelengths. The system under study is an array of identical van der Pol generators in the approximation of quasi-harmonic oscillations.

The features of collective dynamics of oscillators are studied in an ensemble of identical bistable time-delay systems globally coupled via the mean field. The influence of inertial properties and delay of the mean field on the collective dynamics of oscillators is considered. It is shown that a variety of oscillation regimes in the ensemble is caused by the presence of bistable states with considerably different basic frequencies in coupled oscillators.

We study the effects of synchronization and desynchronization in ensembles of phase oscillators with the global Kuramoto–Sakaguchi coupling under common noise driving. Since the mechanisms of synchronization by coupling and by common noise are essentially different, their interplay is of interest.

Dynamics of two phase-locked loops (PLL) with first order low-pass filters coupled via additional phase discriminator is studied. Mathematical models of the partial systems are pendulum-like type. Thus, mathematical model of the whole system consists of four ordinary differential equations. Phase space of the model is a cylindrical with two cyclic variables. In a case of low-inertial control loops the model transforms into dynamical system with toroidal phase space.

The work is devoted to investigation of multistability of running waves in a ring of periodic oscillators with diffusive non-local couplings. It analyzes the influence of long-range couplings and their change with distance on the stability of spatially-periodic regimes with different wave numbers.

We consider dynamics in a pair of nonlinearly coupled pendulums. With existence of dissipation and constant torque such system can demonstrate in-phase periodical rotation in addition to the stable state. We have shown in numerical simulations that such in-