Applied Problems of Nonlinear Oscillation and Wave Theory

Aim. The aim of the study is to formulate an effective model of the power grid, to determine the stable modes of its operation, to identify differences in the considered modes and to test the stability of the system to changes in control parameters, initial conditions and to various types of external influence.

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.

Aim. The aim of the investigation is to study the regularities of phase multistability in an ensemble of oscillatory systems with non-local couplings in dependance of strength and radius of the couplings, as well as to describe them from the point of view of the spatial spectrum.

The paper is devoted to the study of noise-induced intermittent behavior in multistable systems. Such task is an important enough because despite of a great interest of investigators to the study of multistability and intermittency, the problem connected with the detailed understanding of the processes taking place in the multistable dynamical systems in the presence of noise and theoretical description of arising at that intermittent behavior is still remain unsolved.

If we allow non-smooth or discontinuous functions in definition of an evolution operator for dynamical systems, then situations of quasi-hyperbolic chaotic dynamics often occur like, for example, on attractors in model Lozi map and in Belykh map.

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.

We consider an electronic oscillator based on two LC-circuits, one of which includes negative conductivity (the active LC-circuit), where complex dynamics and chaos occur corresponding to the model of wave turbulence of Vyshkind–Rabinovich. The saturation effect for the self-oscillations and their chaotisation take place due to parametric mechanisms due to the presence of a quadratic nonlinear reactive element based on an operational amplifier and an analog multiplier.

Description of real-world systems of interacting units by the means of network model is an effective method of research both in macro- and microscale. In addition, using the simple onelayer networks with one type of connections between the nodes when describing real-world networks is inefficiently because of their complex structural and dynamical nature.

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.