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


Influence of coupling on the dynamics of three delayed oscillators

The purpose of this study is to construct the asymptotics of the relaxation regimes of a system of differential equations with delay, which simulates three diffusion-coupled oscillators with nonlinear compactly supported delayed feedback under the assumption that the factor in front of the feedback function is large enough. Also, the purpose is to study the influence of the coupling between the oscillators on the nonlocal dynamics of the model. Methods. We construct the asymptotics of solutions of the considered model with initial conditions from a special set.

Mixed forced, parametric, and self-oscillations with nonideal energy source and lagging forces

The purpose of this study is to determine the effect of retarded forces in elasticity and damping on the dynamics of mixed forced, parametric, and self-oscillations in a system with limited excitation. A mechanical frictional self-oscillating system driven by a limited-power engine was used as a model. Methods. In this work, to solve the nonlinear differential equations of motion of the system under consideration, the method of direct linearization is used, which differs from the known methods of nonlinear mechanics in ease of use and very low labor and time costs.

Effect of delayed reflection from the remote load on mode competition in а gyrotron

Effect of reflection from the remote load on the mode competition in a two-mode electronic maser is considered. A system of quasilinear equations for slowly varying amplitudes of the modes with cubic nonlinearity where the effect of reflections is taken into account by time delayed terms is analyzed. The most typical case of competition of two modes with close frequencies at the centre of generation zone is studied in detail.

Effect of reflection from remote load on mode competition in gyrotron with quasi­-optical mode convertor

In a gyrotron with quasi-optical mode convertor, apart from the fundamental mode, excitation of a mode with opposite azimuthal rotation of the field occurs due to the wave reflected from the remote load. Interaction of the two oppositely rotating modes is investigated by using the quasi-linear equation for slowly varying amplitudes. The developed theory allows explanation of the experimental results where periodic modulation of the transverse structure of gyrotron radiation partially reflected from a remote oscillating membrane was observed.

Local dynamics of difference and difference-differential equations

We study local dynamics of difference and singular perturbed difference-differential systems in the neighborhood of zero equilibrium state. All critical cases in this problem have infinite dimension. We construct special nonlinear equations that play the role of normal form. Their nonlocal dynamics describes the behavior of solution of initial system.

Study of synchronization in the system of two delay-coupled gyrotrons using a modified quasilinear model

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. Aim.