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Alexander P. Kuznetsov

Publications and source records attributed to Alexander P. Kuznetsov.

10 recordsLinked to original sources
arXiv2021

Analysis of three non-identical Josephson junctions by the method of Lyapunov exponents charts

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 demonstrated. Saddle-node bifurcations of resonant tori are studied with the use of instantaneous Lyapunov exponents. The dependence of the charts on the type of coupling in the system is discussed.

nlin.CD↗
arXiv2015

Four-dimensional system with torus attractor birth via saddle-node bifurcation of limit cycles in content of family of blue sky catastrophes

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 space.

nlin.CD↗
arXiv2015

Oscillations and synchronization in a system of three reactively coupled oscillators

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 of the reactive coupling are discussed.

nlin.CD↗
arXiv2015

Coupled systems with hyperchaos and quasiperiodicity

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 subsystems.

nlin.CD↗
arXiv2014

About hierarchy of multifrequency quasiperiodicity regimes in discrete low-dimensional Kuramoto model

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" parameter plane. The cases of attractive and repulsive interactions are discussed.

nlin.CD↗
arXiv2013

Structure of the eigenfrequencies parameter space for the system of dissipatively coupled oscillators

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 different dimensions is considered. The results for the phase model and for the original system are compared.

nlin.CD↗
arXiv2013

About Landau-Hopf scenario in a system of coupled self-oscillators

The conditions are discussed for which an ensemble of interacting oscillators may demonstrate the Landau-Hopf scenario of successive birth of multi-frequency quasi-periodic motions. A model is proposed that is a network of five globally coupled oscillators characterized by controlled degree of activation of individual oscillators. Illustrations are given for successive birth of tori of increasing dimension via quasi-periodic Hopf bifurcations.

nlin.CD↗
arXiv2008

Properties of synchronization in the systems of non-identical coupled van der Pol and van der Pol - Duffing oscillators. Broadband synchronization

The particular properties of dynamics are discussed for the dissipatively coupled van der Pol oscillators, non-identical in values of parameters controlling the Hopf bifurcation. Possibility of a special synchronization regime in an infinitively long band between oscillation death and quasiperiodic areas is shown for such system. Features of the bifurcation picture are discussed for different values of the control parameters and for the case of additional Duffing-type nonlinearity. Analysis of the abridged equations is presented.

nlin.CD↗