Автоколебания

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.

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.

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.

Regularities of multistability developments are considered in an array of identical self­sustained oscillators with transition to chaos through period­doubling bifurcations. The used model is chain of diffusivelly coupled Rossler oscillators. The number of coexisting regimes are determined through the cascade of the bifurcations. It is shown that regularities of incresing of attractors are defined be transformation of the phase spectrum duing transition to chaos.

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.

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.

In this article Wilson-Cowan model for interactions of excitatory and inhibitory neurons and model of currency oscillations on a Forex market were considered.