Appearance of generalized synchronization in mutually coupled beam-plasma systems

The phenomenon of generalized synchronization onset between mutually coupled beam-plasma systems (Pierce diodes) with supercritical currents has been discovered. It is established that the appearance of a synchronous regime is related to the change in one Lyapunov exponent from a positive to negative value. The results of the analysis are confirmed by the nearest-neighbor method.     

有关混沌及其控制与同步的一些理解

从实例出发，对非线性耗散系统中的混沌及其控制与同步研究中遇到的有关基本概念和问题作一些哲理性解释。内容涉及混沌的基本假设及其标志性特征、通向混沌的道路、混沌系统的相空间基本格局、混沌控制的基本策略、所谓‘混沌同步’以及‘噪声诱导同步’的实质含意、随机混沌的约定性定义、以及数值仿真在混沌研究中的作用等。对混沌及其控制与同步、以及随机混沌提出了一些独特的新见解。     

混沌同步控制策略构造方法研究

水下辐射噪声中的低频线谱是影响潜艇声隐身性能的主要因素,线谱混沌化控制技术通过处于混沌状态的非线性隔振系统将低频线谱转换为宽频混沌谱,可以实现频谱重构并降低线谱强度。前期研究表明,利用广义混沌同步方法可以实现变工况下隔振系统的持续混沌化,在某些情况下还能显著减小振幅,为线谱混沌化控制理论提供了新思路。然而,目前要利用广义混沌同步产生小振幅的持续混沌运动,只能通过"试错"来选择合适的混沌同步控制策略,还没有形成系统的方法。为此,提出了一种混沌同步控制策略构造方法。结合耦合Duffing隔振系统对该构造方法进行验证和说明,并将该方法应用于两自由度非线性隔振系统。     

Dynamic chaos in acoustoelectronic systems

The experimental observation and study of dynamic chaos in acoustoelectronic systems is reported. For these investigations we selected an object, well-known in physical acoustics and acoustoelectronics, in which these new nonlinear properties are observed. This work provides further scope for experimental modeling of stochastic self-excited oscillations. Pis’ma Zh. Tekh. Fiz. 23, 81–85 (May 26, 1997)     

Control of chaos in nonlinear systems with time-periodic coefficients

In this study, some techniques for the control of chaotic nonlinear systems with periodic coefficients are presented. First, chaos is eliminated from a given range of the system parameters by driving the system to a desired periodic orbit or to a fixed point using a full-state feedback. One has to deal with the same mathematical problem in the event when an autonomous system exhibiting chaos is desired to be driven to a periodic orbit. This is achieved by employing either a linear or a nonlinear control technique. In the linear method, a linear full-state feedback controller is designed by symbolic computation. The nonlinear technique is based on the idea of feedback linearization. A set of coordinate transformation is introduced, which leads to an equivalent linear system that can be controlled by known methods. Our second idea is to delay the onset of chaos beyond a given parameter range by a purely nonlinear control strategy that employs local bifurcation analysis of time-periodic systems. In this method, nonlinear properties of post-bifurcation dynamics, such as stability or rate of growth of a limit set, are modified by a nonlinear state feedback control. The control strategies are illustrated through examples. All methods are general in the sense that they can be applied to systems with no restrictions on the size of the periodic terms.     

Control of chaos in nonautonomous systems with quasiperiodic excitation

A procedure is suggested for controlling chaos in quasiperiodically excited systems by stabilizing an unstable torus, or creating a new one by means of a small action. For this purpose the controlled system is synchronized with one which is similar but in a state of stable quasiperiodic motion. The method is illustrated for a quasiperiodically perturbed logistic mapping and a Duffing oscillator. Pis’ma Zh. Tekh. Fiz. 25, 63–70 (August 26, 1999)     

Bifurcation and chaos in power systems

A detailed example of a power system model with load dynamics is studied by investigating qualitative changes or bifurcations in its behaviour as a reactive power demand at one load bus is increased. In addition to the saddle-node bifurcation often associated with voltage collapse, we find other bifurcation phenomena which include Hopf bifurcation, cyclic fold bifurcation, period doubling bifurcation, and the emergence of chaos. The presence of these dynamic bifurcations motivates a re-examination of the role of saddle-node bifurcations in the voltage collapse phenomenon. In fact, simulation results suggest that voltage collapse may take place before the reactive power demand is increased to the system steady-state operating limit where a saddle-node bifurcation is detected. We also consider the role that the algebraic constraints imposed by some load models may play in the global analysis of the attractors of the system. Implications for power system operations are drawn.     

Amplitude modulated chaos in two degree-of-freedom systems with quadratic nonlinearities

Summary Two degree-of-freedom systems with weak quadratic nonlinearities are studied under weak external and parametric excitations respectively. All six possible cases, that arise in the presence of 12 internal resonance, are investigated. The method of averaging is used to obtain a set of four first-order amplitude equations that govern the dynamics of the first-order asymptotic approximation to the response. An analytical technique, based on Melnikov's method is used to predict the parameter range for which chaotic dynamics exists in the undamped averaged system. Numerical studies show that such chaotic responses are quite common in these quadratic systems, and they seem to persist even in the presence of damping.     

Noise-induced binary synchronization in nonlinear systems

The phenomenon of noise-induced binary synchronization has been discovered in two independent dynamical systems generating aperiodic binary signals under the action of a common noise source. The presence of a synchronous regime was confirmed by the calculation of Lyapunov exponents for the two systems. The mechanism of development of the noise-induced binary synchronization regime has been found. A relation of the observed regime to binary generalized synchronization is established.

     

Global bifurcation and chaos in parametrically forced systems with one-one resonance

Global bifurcations of a fourth-order Hamiltonian system with Z₂ ? Z₂ symmetry are studied. The system represents normal-form equations that arise in a variety of problems which have one-one internal resonance and which are forced sinusoidally at the natural frequencies. Four qualitatively different types of global behaviours are shown to occur. Using a generalization of the Melnikov method, three different heteroclinic cycles are shown to break, generating Smale horseshoes and resulting in chaotic phenomena. The theoretical results are verified by numerical simulations. The main conclusion of the analysis is that chaotic phenomena are very common in this class of system     

The volume of information as a measure of the chaos synchronization

A characteristic is suggested for the evaluation of the degree of synchronization of the chaotic oscillations in a system of two coupled oscillators. The proposed value is tested by application to the case of two unidirectionally coupled logistic maps. It is shown that this characteristic is stable with respect to a low noise and a nonlinear distortion of the signal.     

Influencing factors of synchronization in manufacturing systems

Manufacturing systems exhibit two types of synchronisation phenomena: logistics and physics. Previous research has established synchronisation measures for both types and has shown that they are related to the due date performance. However, there is a lack of knowledge about the factors triggering synchronisation emergence as well as a holistic understanding of synchronisation effects on logistics performance. Thus, this research aims to further explore the relation between synchronisation, its influencing factors and its effect on logistics performance. Based on a profound literature review, we derive first hypotheses on the cause-and-effect-relationships between structural and dynamic properties of a manufacturing system and the emergence of logistics and physics synchronisation as well as logistics performance. By conducting a discrete-event simulation study on diverse manufacturing system types (line, flow shop and job shop production), we are able to test these hypotheses. We conclude that manufacturing network architecture as a structural property as well as processing time variability and system workload as dynamic properties may be exploited for an advanced and synchronisation-oriented manufacturing system design.     

Spatiotemporal synchronization of domain oscillations in the system of electroconvection in nematic liquid crystals

The dynamics of a nonstationary pseudo-hexagonal domain structure that appears during the electroconvection in nematic liquid crystals (NLCs) in a constant electric field has been studied using the optical diffraction techniques and the temporal Fourier analysis of the intensity of light transmitted through an NLC cell. The system evolution from an unperturbed state to a regime of developed domain oscillations is traced. It is established that, above the electrohydrodynamic instability threshold, the spatiotemporal synchronization of domain oscillations in a planar NLC layer takes place in the entire sample, which is manifested by the formation of a superlattice with the nodes at the sources of phase waves.     

The synchronization and entanglement of optomechanical systems

We investigate synchronization and entanglement in two coupled cavity optomechanical systems. The classical synchronization, quantum synchronization and entanglement of the two cavity fields and the two mechanical oscillators are analysed, respectively. Our results show that the two cavity resonators are synchronization without entanglement, while the two mechanical oscillators are entangled with quantum-phase synchronization. We conclude that the quantum synchronization and entanglement have no affirmatory relationship although they are both signature of correlation.     

Mutual synchronization and desynchronization of Lorenz systems

The dynamics of two symmetrically coupled Lorenz systems is investigated by means of a numerical experiment. A bifurcation analysis of the synchronization process is presented. The results are compared with numerical experiments. It is shown that changing the coupling can synchronize or desynchronize the subsystems. Pis’ma Zh. Tekh. Fiz. 24, 22–30 (April 12, 1998)     

Phase synchronization of switching processes in stochastic bistable systems

The concept of an analytic signal is used to show that the stochastic synchronization of bistable systems corresponds to locking of the instantaneous phase of the oscillations in complete agreement with the classical theory of phase synchronization. Pis’ma Zh. Tekh. Fiz. 24, 12–19 (August 12, 1998)     

Liquid-phase mass transfer in high-pressure systems with a supercritical and a liquid phase

Liquid-phase diffusion coefficients and mass-transfer coefficients were measured in binary two-phase systems at high pressures. Both were determined from the rates of absorption of the gaseous component into the liquid. Diffusion coefficients were measured by observing unsteady-state diffusion into a sell) i infinite liquid phase and fitting transient counterdiffusion mass-flow rates to the visually determined change of the position of the interface between the liquid and the supercritical phase. Mass-transfer coefficients in the liquid phase were determined from the absorption rate of the gaseous component into a falling liquid film of known flow and physical properties. Experiments were performed with the binary systems carbon dioxide-oleic acid, carbon dioxide -methyl myristate, and carbon dioxide-methyl palmitate. Liquid-phase diffusion coefficients rise significantly with concentration as viscosity decreases. Temperature also has a strong effect on diffusivities. Experimental mass-transfer coefficients in nearly saturated liquids agree well with calculations for falling films with known properties, whereas far from equilibrium, Marangoni convection greatly enhances mass-transfer rates. Close to the critical point of the binary system at a given temperature, a sharp decline of the mass-transfer coefficient is observed.     

Mutual synchronization of switching processes in coupled Lorenz systems

A numerical analysis is made of the synchronization of the mean switching frequencies in two symmetrically coupled Lorenz systems functioning in a chaotic regime. The observed effect on the coupling-mismatch parameter plane corresponds to a region of synchronization of the switching processes, within which the mean switching frequencies coincide to a given accuracy. Pis’ma Zh. Tekh. Fiz. 23, 14–19 (April 26, 1997)     

Behavior of dynamical systems in the regime of transient chaos

The transient chaos regime in a two-dimensional system with discrete time (Eno map) is considered. It is demonstrated that a time series corresponding to this regime differs from a chaotic series constructed for close values of the control parameters by the presence of “nonregular” regions, the number of which increases with the critical parameter. A possible mechanism of this effect is discussed.     

The mean Poincaré return time locking: A criterion of chaos induced synchronization

A new method for diagnostics of the induced synchronization of chaotic self-oscillation is proposed, which is based on the local theory of Poincaré recurrences. It is established that, in the region of synchronization, the mean Poincaré return time is locked by an external harmonic signal.