Generalized synchronization of chaotic oscillators

The behavior of two unidirectionally coupled chaotic oscillators near the boundary of their generalized synchronization is analyzed. Using the modified system method, the position of this boundary on the plane of control parameters is considered and the physical mechanisms leading to the establishment of the generalized synchronization regime are elucidated.     

Generalized synchronization in autooscillatory media

The phenomenon of generalized chaotic synchronization has been found in autooscillatory media described by the Ginzburg-Landau equations. A mechanism responsible for the establishment of generalized synchronization regimes in one-way coupled autooscillatory media exhibiting chaotic spatiotemporal behavior is proposed. The mechanism of generalized synchronization is described based on an analysis of a modified Ginzburg-Landau equation with an additional dissipative term.     

Intermittent generalized synchronization in distributed autooscillatory media described by complex Ginzburg-Landau equations

The appearance of an intermittent regime at the boundary of the generalized chaotic synchronization region has been found for distributed autooscillatory systems described by the complex Ginzburg-Landau equations, which occur in the regime of spatiotemporal chaos. The type of the observed intermittent generalized synchronization behavior is established.     

Synchronization of coupled bistable chaotic systems: experimental study

We carried out an experimental study of the synchronization of two unidirectionally coupled R?ssler-like electronic circuits with two coexisting chaotic attractors. Different stages of synchronization are identified on the route from asynchronous motion to complete synchronization, as the coupling parameter is increased: intermittent asynchronous jumps between coexisting attractors; intermittent anticipating phase synchronization; and generalized synchronization in the form of subharmonic entrainment terminated by complete synchronization. All these regimes are analysed with time-series, power spectra and phase-space plots of the drive and response oscillators. The experimental study implicitly confirms the results of numerical simulations.     

Generalized synchronization in Ginzburg-Landau equations with local coupling

The establishment of generalized chaotic synchronization in Ginzburg-Landau equations unidirectionally coupled at discrete points of space (local coupling) has been studied. It is shown that generalized synchronization regimes are also established with this type of coupling, but the necessary intensity of coupling is significantly higher than that in the case of a spatially homogeneous coupling.     

Generalized synchronization in a system of coupled klystron chaotic oscillators

The phenomenon of generalized chaotic synchronization has been studied in a system of two unidirectionally coupled chaotic oscillators modeling two-sresonator klystron autooscillators. A mechanism explaining the observed behavior is presented.     

Neural networks for large- and small-signal modeling of MESFET/HEMTtransistors

In this paper, we present a comparative study of three neural networks-based solutions for large- and small-signal modeling of MESFET and HEMT transistors. The first two neural architectures are specific for this modeling problem: the generalized radial basis function (GRBF) network, and the smoothed piecewise linear (SPWL) model. These models are compared with the well-known multilayer perceptron (MLP) network. Results are presented for both the large- and small-signal regimes separately. Finally, a global model is proposed that is able to accurately characterize the whole behavior of the transistors. This model is based on a simple combination of the best models obtained for the two kinds of regimes     

The Correctness of Determining the Characteristics of Alternating Generalized Synchronization when Using Only One Variable for Slave and Auxiliary Systems

Technical Physics Letters - A method is considered for distinguishing the typical behavior phases in the mode of alternating generalized synchronization, which is based on the use of an auxiliary...     

Transition to phase synchronization in a system with periodic dynamics under the action of a chaotic signal

Intermittent behavior has been studied near the boundary of phase synchronization in an autooscillatory system with periodic dynamics under the action of an external chaotic signal. It is shown that the intermittency obeys the same scenario as that observed in the case of interaction between two coupled chaotic oscillators.     

横纵激励下几何非线性复合材料层合梁的混沌同步

本文基于里兹-伽辽金法,将考虑几何非线性的一端固支一端夹支复合材料层合梁的控制方程简化为典型的Duffing方程;引入了Duffing-Van Der Pol系统,通过两种系统的分岔图说明了它们共同达到混沌时的参数值;通过广义投影同步法,实现了Duffing系统和Duffing-Van Der Pol系统的精确同步,得到了实现两种系统同步的控制器;分别将两种系统通过Matlab进行了数值仿真,得到了两种系统的同步误差曲线图、二维相图和三维相图,从而验证了混沌同步的准确性。     

Experimental study of the generalized synchronization of chaotic oscillations in the presence of noise

The influence of an external source of noise on the position of the boundary of generalized synchronization (GS) of two unidirectionally coupled chaotic oscillators has been experimentally studied for the first time. It is established that the GS threshold remains unchanged in a broad range of the external noise intensity, i.e., the GS regime is stable with respect to external noise.     

On the longitudinal vibrations of a bar with viscous boundaries: Super-stability,super-instability,and loss of damping

This paper presents the investigation of the longitudinal motions of a bar subjected to viscous boundary conditions at each end. These viscous boundary conditions can also be thought of in terms of boundary feedback control. The system is not self-adjoint and for certain parameter regimes exhibits super-stable, super-unstable, and undamped behavior. Closed form solutions to the response of the system subjected to initial conditions and external excitation are obtained. The physical origins of the super-stable and super-unstable behavior are investigated and their intricate connectedness with the continuum model used to understand the dynamics is explained. The issue of discretization of the continuous system is discussed and it is shown that the continuum assumption bestows certain features to the response of the system that no finite dimensional approximation can qualitatively capture. Computational results corroborating the theoretical analysis are presented.     

Effects of unwanted feedback on synchronized chaotic optical communications

The effects of unwanted external optical feedback on synchronized chaotic optical communication systems are studied numerically. We consider an open-loop configuration consisting of a transmitter laser with double external optical feedbacks and a receiver laser with optical injection from the transmitter laser. First, including the effects of unwanted optical feedback, the synchronization performances of both the complete synchronization and the generalized synchronization are examined. Then the encoding and decoding performances of the generalized synchronization and the effects of the introduced feedback are investigated, respectively. Finally, we study the control of the unwanted feedback on the dynamics of the transmitter laser and briefly discuss the system security when the transmitter laser is driven to operate in a steady state or periodic oscillation state by the additional feedback.     

Convection in a Two-Layer System with a Deformable Interface Under Low Gravity Conditions

The onset of thermal convection in a system of two horizontal layers of immiscible liquids of similar densities is studied under low gravity conditions. A constant heat flux is prescribed at both rigid boundaries. A generalized Boussinesq approach that allows correct accounting for the interface deformation is used. The long-wave perturbations emerge under low-gravity conditions; either monotonic or oscillatory modes are critical depending on the problem. Moreover, two different modes of the monotonic instability exist. For the first instability mode, the convection dominates, whereas the interface remains nearly undeformable. The second monotonic instability mode is substantially related to interface deformations. The system of non-linear amplitude equations describing the behavior of long-wave regimes at finite-amplitude interface deflection and finite supercriticalities is obtained. The analytical and numerical investigations of these equations show that the stable non-trivial stationary solutions are absent, and after a transient at least one of the layers is split into the areas not connected to each other. The nonlinear regimes of cellular convection are studied numerically by the Level Set method.     

Transverse vibration of rotary tapered microbeam based on modified couple stress theory and generalized differential quadrature element method

The transverse vibration of a rotary tapered microbeam is studied based on a modified couple stress theory and Euler–Bernoulli beam model. The governing differential equation and boundary conditions are derived according to Hamilton's principle. The generalized differential quadrature element method is then used to solve the governing equation for cantilever and propped cantilever boundary conditions. The effect of the small-scale parameter, beam length, rate of cross-section change, hub radius, and nondimensional angular velocity on the vibration behavior of the microbeam is presented.     

Features of induced synchronization of a bistable oscillator with chaotic dynamics

The features of induced synchronization of a Chua oscillator with a nonlinear element admitting cubic approximation have been numerically simulated for a system where the autonomous operation admits regular or chaotic regimes determined by losses in the oscillatory circuit. The cases of deterministic synchronization (under the action of a harmonic external driving signal) and chaotic synchronization (chaotic control) have been considered. It is established that, outside the band of synchronous oscillations that corresponds to the deterministic synchronization, the external harmonic signal stimulates the transformation of regular oscillations into chaos with the motions switched between two attractors. In cases of chaotic synchronization, there is a residual “noise” in the form of differential chaotic oscillations, which grows with increasing non-identity of the driving and driven signals.     

Finite-element modeling of rate dependent mechanical properties in nanocrystalline materials

A generalized self-consistent polycrystal model is used to study the mechanical properties of polycrystalline metals as the grain size decreases from the ultra-fine size to the nanometer scale. The model takes each oriented grain and its immediate grain boundary to form a pair. Then by making use of a composite model, the nonlinear behavior of the nanocrystalline polycrystal is determined. The finite-element method is employed in conjunction with the unit cell of the composite to investigate the rate-dependent tensile behavior of the system. A dislocation density based constitutive equation is used to describe the plastic flow behavior of the grain interior. The boundary phase is assumed to have the mechanical properties of quasi-amorphous material. The constitutive equations for both grain interior and boundary phase are implemented into a finite-element program and the results of the calculations are compared with previously published experimental data. For some cases, an optimization procedure was used to tune some parameters of the model in order to decrease the distance between the calculated and experimental stress–strain curves. The agreement between results indicates the suitability of the updated model for nanocrystalline materials.     

Method for separating laminar and turbulent intervals in intermittent time series of systems near the phase synchronization boundary

A new method is proposed for separating the intervals of synchronous (laminar) and asynchronous (turbulent) behavior in intermittent time series of coupled chaotic systems occurring near the boundary of the phase synchronization regime. Using this method, it is possible to determine the durations of turbulent and laminar intervals, which are necessary for an analysis of the statistical characteristics of a given dynamical system. The proposed approach directly employs the instantaneous phases of chaotic signals and provides exact values of the durations of turbulent and laminar intervals in the system behavior. The validity of the new method is verified by a comparison of the results to analogous data obtained previously, which shows their good agreement.     

Synchronization of quasi-periodic oscillations in coupled phase oscillators

The phenomenon of synchronization of two oscillators under the action of an external force has been studied in a phase approximation. The Lyapunov maps are presented and the possible types of regimes are considered. Various types of two-frequency tori are revealed and classified.     

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.