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


Нормализованные краевые задачи в модели оптико-электронного осциллятора с запаздыванием

Исследуется динамика оптико-электронного осциллятора с запаздывающей обратной связью в окрестности нулевого состояния равновесия. Дифференциально-разностная модель содержит малый параметр при старшей производной. Показано, что в определенной окрестности точки бифуркации число корней характеристического уравнения с близкой к нулю действительной частью неограниченно возрастает при уменьшении малого параметра.

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

In a gyrotron with quasi­optical 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 quasi­linear 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.

Hyperbolic chaos in the Bonhoeffer–van der Pol oscillator with additional delayed feedback and periodically modulated excitation parameter

Topic and aim. The aim of the work is to consider an easy-to-implement system demonstrating the Smale–Williams hyperbolic attractor based on the Bonhoeffer–van der Pol oscillator, alternately manifesting a state of activity or suppression due to periodic modulation of the parameter by an external control signal, and supplemented with a delayed feedback circuit. Investigated models. A mathematical model is formulated as a non-autonomous second-order equation with delay. The scheme of the electronic device that implements this type of chaotic behavior is proposed.