# Автоколебания

## Phenomenon of the van der pol equation

This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radioengineering, physics and mathematics. The review outlines only one essential point of his work, associated with the equation that bears his name, and has a surprisingly wide range of applications in natural sciences. In this review we discuss the following matters. • The biography of van der Pol, history of his equation and supposed precursors. • The contribution of A.A. Andronov in the theory of selfoscillations.

## Reflex klystron as an example of a selfoscillating delayed feedback system

Nonstationary theory of the reflex klystron oscillator based on differential equation with delay is developed. Analysis of selfexcitation conditions, steadystate oscillation regimes and their stability is presented. Application of the developed theory for calculating of output characteristics of micromachined submillimetreband reflex klystron is presented as well. Theoretical results are compared with the results of numerical simulation based on the particleincell method.

## Coupled selfsustained oscillators of different nature by example of van der pol system and brusselator

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.

## Research of dynamic modes in the mathematical model of elementary thalamocortical cell

In the work the mathematical model of the thalamocortical network’s unit cell and it’s characteristic dynamical modes in system, describing the interaction between a thalamus, thalamus reticular nucleus and a cortex, is studied. During normal information processing, input signal gating occurs in time in the thalamo-cortical network. The violation of the normal functioning leads to an epilepsy, when the perception of information is disrupted.

## COMPLEX DYNAMICS AND CHAOS IN ELECTRONIC SELF-OSCILLATOR WITH SATURATION MECHANISM PROVIDED BY PARAMETRIC DECAY

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.