A. P. Kuznetsov

Features of the synchronization of coupled van der Pol oscillators with nonidentical control parameters

The possibility of broadband synchronization in a system of dissipatively coupled van der Pol oscillators with different parameters controlling the Andronov-Hopf bifurcation is considered.

The Death of Quasi-Periodic Regimes in a System of Dissipatively Coupled van der Pol Oscillators under Pulsed Drive Action

We have studied a system of coupled van der Pol oscillators under pulsed drive action. In the case where the coupled oscillators exhibit the death of oscillations, the introduction of a pulsed drive leads to the appearance of islands corresponding to quasi-periodic regimes in the drive period-amplitude plane, which are also dying with an increase in the frequency detuning.

Features of Short-Pulse Synchronization of a Lorenz System

The pattern of synchronization of a Lorenz system by a periodic sequence of short pulses has been studied during the variation of a parameter determining the appearance of a chaotic attractor.

Stabilizing the Rössler system by external pulses on a runaway trajectory

The action of external pulses on the Rössler system prior to the onset of a saddle-node type bifurcation on a runaway trajectory is considered. It is shown that a pulsed drive can lead to the appearance of stable periodic and quasi-periodic regimes in the nonautonomous system.

Features in dynamics of an almost conservative Ikeda map

Dynamics of the Ikeda map has been studied under conditions of very small dissipation, both in the autonomous regime and in the presence of an external noise signal. It is established that the system has a large number of coexisting low-period attractors (the lower the dissipation in the system, the greater the number of such attractors) and exhibits a rather long transient process. The action of an external noise leads to the breakage of most attractors.

Features of pulsed synchronization of an autooscillatory system with a three-dimensional phase space

The patterns of pulsed synchronization of an autooscillatory system with the limit cycle embedded in a three-dimensional phase space are considered.

Forced Synchronization in a System with Unstable Cycle

The dynamics of a system with unstable limiting cycle under the action of a periodic sequence of delta pulses is considered. It is shown that stable quasiperiodic regimes and phase lock regimes (synchronization) can be observed within a narrow range of parameters of the external signal.

Quasi-Periodic Regimes in the Transition to Unstable Lagrange Dynamics

The appearance of a narrow band of quasi-periodic regimes between the regions of periodic (stable) and unstable (in the Lagrange sense) dynamics in the space of parameters of a dynamical system has been studied in the case of a model two-dimensional Hénon map. It is established that fast breakage of a quasi-periodic regime proceeds via nonlocal bifurcation, whereby an attractor touches a stable manifold of an immobile saddle point.

The planes of control parameters of coupled nonidentical autooscillatory systems

Bifurcation lines and synchronization regions on the planes of control parameters of two-or three-dimensional coupled nonidentical autooscillatory systems are analyzed. A special structure of synchronization regions and a new type of critical behavior during the transition to chaos in coupled systems featuring period-doubling bifurcations are revealed.

On the Scaling Properties of Two Unidirectionally Coupled Period-Doubling Systems in the Presence of Noise

The results of numerical experiments reveal and illustrate the scaling properties manifested under the noise action at a bicritical point situated at the chaos boundary in a system of two unidirectionally coupled subsystems featuring the period doubling.