# A. P. KuznetsovKotel'nikov Institute of Radioengineering and Electronics

A. P. Kuznetsov

Doctor of Sciences

## About

210

Publications

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1,312

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Introduction

**Skills and Expertise**

## Publications

Publications (210)

The problem of growing complexity of the dynamics of the coupled phase oscillators as the number of oscillators in the chain increases is considered. The organization of the parameter space (parameter of the frequency detuning between the second and the first oscillators versus parameter of dissipative coupling) is discussed. The regions of complet...

Synchronization in the system of coupled non-identical non-isochronous van der Pol–Duffing oscillators with inertial and dissipative coupling is discussed. Generalized Adler’s equation is obtained and investigated in the presence of all relevant factors affecting the synchronization (non-isochronism of the oscillators, their non-identity, coupling...

The term 'hidden attractor' relates to a stable periodic, quasiperiodic or chaotic state whose basin of attraction does not overlap with the neighborhood of an unstable equilibrium point. Considering a three-dimensional oscillator system that does not allow for the existence of an equilibrium point, this paper describes the formation of several dif...

We propose a new three-dimensional map that demonstrates the two-and three-frequency quasi-periodicity. For this map, all basic quasi-periodic bifurcations are possible. The study was realized by using Lyapunov charts completed by plots of Lyapunov exponents, phase portraits and bifurcation trees illustrating the quasi-periodic bifurcations. The fe...

A model of a generator of quasiperiodic oscillations forced by a periodic pulse sequence is studied. We analyze synchronization when the autonomous generator demonstrates periodic, quasiperiodic, re-spective weakly chaotic oscillations. For the forced quasiperiodic os-cillations a picture of synchronization, consisting of small-scale and large-scal...

We consider the hierarchical organization of the parameter space of four coupled phase oscillators. The structure of the complete synchronization and quasi-periodicity regions of different dimensions are studied. The bifurcation mechanisms of destruction of full and partial synchronizations are discussed.

A system of three non-identical Josephson junctions connected via an RLC circuit is considered. The method of Lyapunov exponents charts is used, which makes it possible to identify the main types of dynamics of the system and to analyze the dependence of its properties on parameters. The possibility of both two and three-frequency invariant tori is...

Appearance of chaotic dynamics as a result of multi-frequency tori destruction is carried out on the example of a model of a multimode generator. Quasiperiodic bifurcations occurring with multi-frequency tori are discussed in the context of the Landau-Hopf scenario. Structure of the parameter space is studied, areas with various chaotic dynamics, i...

Background and Objectives: The basic model of study is the simplest three - dimensional map with two-frequency and three-frequency quasiperiodicity at adding of noise. The main objective is to examine the effect of noise on the quasiperiodic Hopf bifurcation of the 3-torus birth. Materials and Methods: To study the torus map in the presence of nois...

Using an example a system of two coupled generators of quasiperiodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involve saddle tori occurring at their...

An ensemble of van der Pol oscillators coupled in a ring has been numerically simulated. Peculiarities of chaotic dynamics have been studied by analysis of Fourier spectra and Lyapunov exponents. It is established that chaotic dynamics appearing upon the breakup of multifrequency tori is characterized by a broadband spectrum.

Using an example of a radiophysical generator model, scenarios for the formation of various chaotic attractors are described, including chaos and hyperchaos. It is shown that as a result of a secondary Neimark–Sacker bifurcation, a hyperchaos with two positive Lyapunov exponents can occur in the system. A comparative analysis of chaotic attractors...

A problem of synchronization of quasiperiodic oscillations is discussed in application to an example of coupled systems with autonomous quasiperiodic dynamics. Charts of Lyapunov exponents are presented that reveal characteristic domains on the parameter plane such as oscillator death, complete synchronization, phase synchronization of quasiperiodi...

We propose a multicircuit oscillator with a common control scheme driving self-sustained oscillations in each circuit, which can exhibit quasi-periodic and chaotic oscillations. The proposed oscillator was investigated by experimental and numerical methods that confirmed the possibility of exciting multifrequency quasi-periodic, chaotic, and hyperc...

Dynamics of chains of three and four coupled non-identical Josephson junctions is considered. Synchronization effects are discussed including resonance Arnold web formation on the base of tori of different dimensions.

We propose a multicircuit oscillator with a common control scheme driving self-sustained oscillations in each circuit, which can exhibit quasi-periodic and chaotic oscillations. The proposed oscillator was investigated by experimental and numerical methods that confirmed the possibility of exciting multifrequency quasi-periodic, chaotic, and hyperc...

Subject of the study. Recently, the problems of synchronization of systems demonstrating quasi-periodic oscillations arouse interest. In particular, it can be generators of quasi-periodic oscillations that allow a radiophysical realization. In this paper we consider the dynamics of two coupled oscillators of quasi-periodic oscillations with a singl...

We discuss the effect of noise on a system with a quasi-periodicity of different dimensions. As the basic model of our research we use the simplest three-dimensional map with two-frequency and three-frequency quasi-periodicity. Modification of the dynamical regimes at the influence of noise is considered with the help of Lyapunov chart method. The...

Five van der Pol oscillators connected into a ring have been investigated numerically. We have considered different types of coupling: dissipative and active, as well as dissipative and active with a single coupling sign reversal. Bifurcations observed upon a transition from a five-to four-frequency torus have been investigated. The possibility of...

The dynamics of two coupled twist maps with weak dissipation is studied. The calculation of Lyapunov exponents is used to analyze the structure of the action plane of the system. The chaotic transient dynamics is revealed for extremely small values of dissipation by calculation of finite-time Lyapunov exponents. The stagger-and-step method is used...

В работе обсуждается построение удобных и информационно емких трехмерных отображений, демонстрирующих существование 2-торов и 3-торов. Первое отображение получено путем дискретизации потоковой системы – генератора квазипериодических колебаний. Второе – путем дискретизации климатической модели Лоренц-84. Третье отображение предложено в теории квазип...

We suggest a new technique of fold Poincaré section, allowing one to visualize an invariant curve of a multi-frequency invariant torus in a physical experiment. Details of the technique are presented, along with examples of its application to various experimental studies. Examples of how an invariant curve is visualized in double-, triple-and four-...

A model with hyperchaos is studied by means of Lyapunov two-parameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the parameter plane of coupled sys- tems, corresponding to the cases of interaction of quasiperiodic and hyperchaotic su...

We propose a new three-dimensional map that demonstrates the two- and
three-frequency quasi-periodicity. For this map all basic quasi-periodic
bifurcations are possible. The study was realized by using method of Lyapunov
charts completed by plots of Lyapunov exponents, phase portraits and
bifurcation trees illustrating the quasi-periodic bifurcatio...

We propose a new three-dimensional map that demonstrates the two- and three-frequency quasi-periodicity. For this map all basic quasi-periodic bifurcations are possible. The study was realized by using method of Lyapunov charts completed by plots of Lyapunov exponents, phase portraits and bifurcation trees illustrating the quasi-periodic bifurcatio...

We consider a system of three interacting van der Pol oscillators with reactive coupling. Phase equations are derived, using proper order of expansion over the coupling parameter. The dynamics of the system is studied by means of the bifurcation analysis and with the method of Lyapunov exponent charts. Essential and physically meaningful features o...

Examples of mechanical systems are discussed, where quasi-periodic motions may occur, caused by an irrational ratio of the radii of rotating elements that constitute the system. For the pendulum system with frictional transmission of rotation between the elements, in the conservative and dissipative cases we note the coexistence of an infinite numb...

A new four-dimensional model with quasi-periodic dynamics is suggested. The
torus attractor originates via the saddle-node bifurcation, which may be
regarded as a member of a bifurcation family embracing different types of blue
sky catastrophes. Also the torus birth trough the Neimark-Sacker bifurcation
occurs in some other region of the parameter...

The phenomenon of hard excitation is natural for many electronic oscillators. In particular, in a gyrotron, a maximal efficiency is often attained in the hard excitation regime. In this paper, we study the injection-locking phenomena using two models of an electronic maser in the hard excitation mode. First, bifurcation analysis is performed for th...

The hydrodynamic equations of inviscid compressible fluid are converted to a
form suitable for development of self-consistent theory of interaction of hydrodynamic
flows with resonators and periodic structures by analogy with the theory of microwave
electronics devices with crossed electric and magnetic fields. We consider excitation of
the acousti...

We discuss the effect of weak dissipation on the system with Arnold diffusion which consists of two coupled twist maps. The finite time Lyapunov exponents are used to analyze the dynamics. We observe the phenomenon of transient chaos and changes in the phase space structure including the disappearance of some resonances. © 2015, Education and Upbri...

We consider a system of three interacting van der Pol oscillators with reactive coupling. Phase equations are derived, using proper order of expansion over the coupling parameter. The dynamics of the system is studied by means of the bifurcation analysis and with the method of Lyapunov exponent charts. Essential and physically meaningful features o...

Книга содержит более 200 оригинальных физических задач, предлагавшихся в разные
годы на олимпиадах школьников по физике в г. Саратове.
.

Synchronization of forced reactively coupled van der Pol oscilla-tors is investigated in the phase approximation. We discuss essential features of the reactive coupling. Bifurcation mechanisms for the destruction of complete synchronization and possible quasi-periodic regimes of different types are revealed. Regimes when autonomous oscillators demo...

A model with hyperchaos is studied by means of Lyapunov two-parameter
analysis. The regions of chaos and hyperchaos, as well as autonomous
quasiperiodicity are identified. We discuss the picture of domains of different
regimes in the parameter plane of coupled systems, corresponding to the cases
of interaction of quasiperiodic and hyperchaotic subs...

Ensembles of several Rössler chaotic oscillators are considered. We show that a typical phenomenon for such systems is an emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains...

We consider a system of three interacting van der Pol oscillators with
reactive coupling. Phase equations are derived, using proper order of expansion
over the coupling parameter. The dynamics of the system is studied by means of
the bifurcation analysis and with the method of Lyapunov exponent charts.
Essential and physically meaningful features o...

Synchronization of forced reactively coupled van der Pol oscillators is
investigated in the phase approximation. We discuss essential features of the
reactive coupling. Bifurcation mechanisms for the destruction of complete
synchronization and possible quasi-periodic regimes of different types are
revealed. Regimes when autonomous oscillators demon...

We consider a network of four non-identical chaotic Rössler oscillators. The possibility is shown of appearance of two-, three-and four-frequency invariant tori resulting from secondary quasi-periodic Hopf bifurcations and saddle-node homoclinic bifurcations of tori. PACS numbers: 05.45.Pq, 05.45.Xt

The dynamics of three coupled chaotic Rössler systems is considered. We discuss scenarios for the evolution of different types of regimes. The possibility of two- and three-frequency quasi-periodicity is shown. We considered the occurrence of resonanses on three-frequency torus, which leads to two-freqiency quasi-periodic regimes. The illustrations...

The dynamics of a low-dimensional ensemble consisting of a network of five discrete phase oscillators is considered. A two-parameter synchronization picture, which appears instead of the Arnol'd tongues with an increase of the system dimension, is discussed. An appearance of the Arnol'd resonance web is detected on the "frequency – coupling" parame...

We demonstrate scopes of a method of Lyapunov charts for identification of different regimes in nonlinear systems. We show that Lyapunov charts reveal fine and complex structure of the parameter space. Illustrations are given for the ensembles of coupled self-oscillating elements of van der Pol type oscillator and also for the coupled phase oscilla...

Background: Regulation of the blood flow to the individual functional unit (nephron) of the kidney involves a feedback mechanism that produces large-amplitude oscillations in the blood flow itself as well as in the intra-nephron pressures and flows. Neighboring nephrons adjust their blood flow variations relative to one another via signals that pro...

A dynamics of a low-dimensional ensemble consisting of connected in a network
five discrete phase oscillators is considered. A two-parameter synchronization
picture which appears instead of the Arnold tongues with an increase of the
system dimension is discussed. An appearance of the Arnol'd resonance web is
detected on the "frequency - coupling" p...

1. Введение Задачи, связанные с синхронизацией, как небольшого числа лазеров, так и достаточно больших их массивов, весьма популярны в лазерной физике [1-11]. Синхронизация позволяет существенно увеличить интенсивность и качество излучения. Добиться синхронной генерации лазеров можно разными способами. Это может быть инжекция внешнего поля от одноч...

The dynamics of the four dissipatively coupled van der Pol oscillators is considered. Lyapunov chart is presented in the parameter plane. Its arrangement is discussed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators. Here are quasi-periodic saddle-node, Hopf and Neimark–Sacker bifurcations. The effec...

We study the dynamics of two conservatively coupled Hénon maps at different levels of dissipation. It is shown that the decrease of dissipation leads to changes in the structure of parameter plane and the scenarios of transition to chaos compared to the case of infinitely strong dissipation. Particularly, the Feigenbaum line becomes divided into se...

Настоящий обзор посвящен знаменитому голландскому ученому Балтазару ван дер - Полю, который внес ощутимый вклад в развитие радиотехники, физики и математики. В обзоре выделен лишь один момент его творчества, связанный с уравнением, носящим его имя, и удивительно широким диапазоном применения этого уравнения в естествознании. В обзоре изложены следу...

Ensembles of several Rössler chaotic oscillators are considered. We show that a typical phenomenon for such systems is an emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bi-furcations based on tori of increasing dimension is demonstrated. The domains...

The effect of small nonlinear dissipation on the dynamics of system with
stochastic web which is linear oscillator driven by pulses is studied. The
scenario of coexisting attractors evolution with the increase of nonlinear
dissipation is revealed. It is shown that the period-doubling transition to
chaos is possible only for third order resonance an...

Considering a family of three-dimensional oscillators originating in the field of radio-engineering, the paper describes three different mechanisms of torus formation. Particular emphasis is paid to a process in which a saddle-node bifurcation eliminates a stable cycle and leaves the system to find a stationary state between a saddle cycle and a pa...

Structure of the eigenfrequencies parameter space for three and four
dissipatively coupled van der Pol oscillators is discussed. Situations of
different codimension relating to the configuration of the full synchronization
area as well as a picture of different modes in its neighborhood are revealed.
The organization of quasi-periodic areas of diff...

We study the dynamics of two conservatively coupled H\'enon maps at different
levels of dissipation. It is shown that the decrease of dissipation leads to
changes in the parameter plane structure and scenarios of transition to chaos
comparing with the case of infinitely strong dissipation. Particularly, the
Feigenbaum line becomes divided into seve...

We considered the discrete map with quasi-periodic dynamics in the wide band of
the parameters and investigated the structure of the parameter plane of two coupled maps.
We revealed the doublings of 3D-tori, the systems of 2D-tori and synchronization tongues
and the resonance web. Also we revealed the attractors with complex structure and the
large...