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

Методические заметки по нелинейной динамике

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.

Low-­order dynamical models for vortical flows of inviscid fluid in square area

The Galerkin method together with the method of small parameter is applied for study of Routh­like equations describing the dynamics of two­dimensional inviscid incom­pressible fluid flows. A set of simple models for some vortical flows of such fluid in rectangular area has been derived and analysed.

Nonlinear random waves in fluid, and the main mechanism of their excitation

To describe the problem of the random nonlinear waves in fluid, we must know, exactly or approximately, how occurs the process of the vortex separation. For this it is conveniently to use models based on physical considerations and (or) some experimental data. The main attention in this review will be attended to random waves, emerging, for example, at stall flutter. Such waves often appear in fluid, and they are the main cause of many disasters is seas and oceans.

Chaotic dynamics of hunt model – artificially constructed flow system with a hyperbolic attractor

We study numerically chaotic behavior associated with the presence of a hyperbolic strange attractor of Plykin type in the model of Hunt, that is an artificially constructed dynamical system with continuous time. There are presented portraits of the attractor, plots of realizations for chaotic signal generated by the system, illustrations of the sensitive dependence on initial conditions for the trajectories on the attractor. Quantitative characteristics of the attractor are estimated, including the Lyapunov exponents and the attractor dimension.

Period doubling maps with driving parameter modulated by delayed feedback

It was shown that addition of modulation of driving parameter with using delay can be considered as physically reasoned method of construction two-dimensional maps with non?xed Jacobian. The examples of such two-parameter and three-parameter maps were presented. The conditions of Neumark–Sacker’s bifurcation, period doubling and resonance 1:2 were obtained. The structure of parameter space was studied by dynamical regimes maps method and the regions of quasiperiodic regimes and di?erent synchronous regimes were revealed.

Calculation technique of starting current of multicavity klystron autogenerators

On the base of the cascade-bunching theory the calculation technique of starting current of multicavity klystron autogenerators is presented in this paper.  

Experimental research of synchronization of two-frequency quasiperiodic motions

We present the electronic scheme of autonomous generator of two-frequency quasiperiodic motions and the experimental research results of e?ect of quasi-periodic motions synchronization under the external two-frequency force.

How force to sound the numerical experiment results

The unusual technique of interpretation of numerical experiment results as sound waves is o?ered. Recommendations for practical implementation of the o?ered technique and for its application in various areas of research, designer and educational activity are given.

Canonical models of nonlinear dynamics in economics

This paper is the book review. Its main purpose is to show that practically all kinds of canonical models of nonlinear dynamics are used in the present mathematical economics.   

Conservative and dissipative dynamics of ikeda map

Di?erent methods for investigation of dissipative, nearly conservative and conservative systems have been demonstrated on the example of Ikeda map. The method for two-parameter analysis of dynamics of conservative systems has been proposed. Signi?cant changes in the structure of the parameter and phase space of Ikeda map when dissipation decreases have been revealed. Tasks for seminars and computer practices have been proposed.