744 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- V. A. Sablikov41 · h 11
- K. Nagaev32 · h 13
- S. Zaitsev-Zotov30 · h 15
- A. Volkov2 profiles29 · h 30
- P. Monceau2 profiles27 · h 37
- V. Koshelets2 profiles26 · h 31
- D. S. Shapiro25 · h 10
- V. Enaldiev2 profiles22 · h 16
- Vladimir A. Volkov21 · h 14
- A. Sinchenko2 profiles20 · h 12
- S. Nikitov3 profiles20 · h 33
- S. Artemenko19 · h 17
- Russian Academy of SciencesRU201 papers
- Moscow Institute of Physics and TechnologyRU95 papers
- Centre National de la Recherche ScientifiqueFR40 papers
- Lomonosov Moscow State UniversityRU40 papers
- National University of Science and TechnologyRU39 papers
- Saratov State UniversityRU31 papers
- Landau Institute for Theoretical PhysicsRU29 papers
- All Russia Research Institute of AutomaticsRU27 papers
- National Research University Higher School of EconomicsRU27 papers
- Ruhr University BochumDE24 papers
- Karlsruhe Institute of TechnologyDE22 papers
- National Research Nuclear University MEPhIRU20 papers
31 papers · 1 filter
On Hyperbolic Attractors in Complex Shimizu -- Morioka Model
V. P. Kruglov, I. R. Sataev
We present a modified complex-valued Shimizu -- Morioka system with uniformly hyperbolic attractor. The numerically observed attractor in Poincaré cross-section is topologically cl…
On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators
Evgeny A. Grines, Alexey O. Kazakov, Igor R. Sataev
We study chaotic dynamics in a system of four differential equations describing the dynamics of five identical globally coupled phase oscillators with biharmonic coupling. We show…
Dynamics of Non-Autonomous Oscillator with a Controlled Phase and Frequency of External Forcing
Darina Krylosova, Evgeny Seleznev, Nataliya Stankevich
The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and freq…
Smale-Williams Solenoids in a System of Coupled Bonhoeffer-van der Pol Oscillators
V. M. Doroshenko, V. P. Kruglov, S. P. Kuznetsov
The principle of constructing a new class of systems with hyperbolic chaotic attractors is proposed. It is based on using oscillators, the transfer of excitation between which is p…
Lyapunov analysis of strange pseudohyperbolic attractors: angles between tangent subspaces, local volume expansion and contraction
Pavel V. Kuptsov, Sergey P. Kuznetsov
In this paper we analyze local structure of several chaotic attractors recently suggested in literature as pseudohyperbolic. The absence of tangencies and thus the presence of the…
Numerical test for hyperbolicity in chaotic systems with multiple time delays
Pavel V. Kuptsov, Sergey P. Kuznetsov
We develop an extension of the fast method of angles for hyperbolicity verification in chaotic systems with an arbitrary number of time-delay feedback loops. The adopted method is…
Strange Nonchaotic Self-Oscillator
Alexey Yu. Jalnine, Sergey P. Kuznetsov
An example of strange nonchaotic attractor (SNA) is discussed in a dissipative system of mechanical nature driven by constant torque applied to one of the elements of the construct…
From geodesic flow on a surface of negative curvature to electronic generator of robust chaos
Sergey P. Kuznetsov
Departing from the geodesic flow on a surface of negative curvature as a classic example of the hyperbolic chaotic dynamics, we propose an electronic circuit operating as a generat…
Numerical test for hyperbolicity of chaotic dynamics in time-delay systems
Pavel V. Kuptsov, Sergey P. Kuznetsov
We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions bet…
The simplest map with three-frequency quasi-periodicity and quasi-periodic bifurcations
A. P. Kuznetsov, Yu. V. Sedova
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…
Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories
Sergey P. Kuznetsov
Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt --…
Oscillations and synchronization in a system of three reactively coupled oscillators
Alexander P. Kuznetsov, Ludmila V. Turukina, Nikolai Yu. Chernyshov +1
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.…
Attractor of Smale-Williams type in autonomous distributed system
Vyacheslav P. Kruglov, Sergey P. Kuznetsov, Arkady Pikovsky
We consider an autonomous system of partial differential equations for one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternatin…
Hyperbolic and non-hyperbolic chaos in a pair of coupled alternately excited FitzHugh-Nagumo systems
Alexey Yu. Jalnine
We investigate a possibility of realization of structurally stable chaotic dynamics in neural systems. The considered model of interacting neurons consists of a pair of coupled Fit…
Structure of the eigenfrequencies parameter space for the system of dissipatively coupled oscillators
Yulia P. Emelianova, Alexander P. Kuznetsov, Ludmila V. Turukina +2
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…
About Landau-Hopf scenario in a system of coupled self-oscillators
Alexander P. Kuznetsov, Sergey P. Kuznetsov, Igor R. Sataev +1
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…
Hyperbolic chaos at blinking coupling of noisy oscillators
Pavel V. Kuptsov, Sergey P. Kuznetsov, Arkady Pikovsky
We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where one-cluster and two-cluster synchronous states alternate. In the thermodynamic…
Different types of critical behavior in conservatively coupled Hénon maps
D. V. Savin, A. P. Kuznetsov, A. V. Savin +1
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 parameter pl…
A "saddle-node" bifurcation scenario for birth or destruction of a Smale-Williams solenoid
Olga B. Isaeva, Sergey P. Kuznetsov, Igor R. Sataev
Formation or destruction of hyperbolic chaotic attractor under parameter variation is considered with an example represented by Smale--Williams solenoid in stroboscopic Poincaré ma…
Hyperbolic Chaos of Turing Patterns
Pavel V. Kuptsov, Sergey P. Kuznetsov, Arkady Pikovsky
We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation long…
Electronic circuits manifesting hyperbolic chaos and their simulation with software package Multisim
Sergey P. Kuznetsov
We consider several electronic circuits, which represent dynamical systems with hyperbolic chaotic attractors of Smale-Williams type, and demonstrate results of their simulation us…
On the road towards multidimensional tori
A. P. Kuznetsov, I. R. Sataev, L. V. Turukina
The problem of persistence of four-frequency tori is considered in models represented by the coupled periodically driven self-oscillators. We show that the adding the third oscilla…
Collective Phase Chaos in the Dynamics of Interacting Oscillator Ensembles
Sergey P. Kuznetsov, Arkady Pikovsky, Michael Rosenblum
We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, wh…
A non-autonomous flow system with Plykin type attractor
Sergey P. Kuznetsov
A non-autonomous flow system is introduced with an attractor of Plykin type that may serve as a base for elaboration of real systems and devices demonstrating the structurally stab…