Populations of coupled electrochemical oscillators

Experiments were carried out on arrays of chaotic electrochemical oscillators to which global coupling, periodic forcing, and feedback were applied. The global coupling converts a very weakly coupled set of chaotic oscillators to a synchronized state with sufficiently large values of coupling strength; at intermediate values both intermittent and stable chaotic cluster states occur. Cluster formation and synchronization were also obtained by applying feedback and forcing to a moderately coupled base state. The three cases differ, however, in other details. The feedback and forcing also produce periodic cluster states and more than two clusters. Configurations of two (chaotic) clusters and two, three, or four (periodic) clusters were observed. (c) 2002 American Institute of Physics.     

Chaos dynamics in vertical-cavity surface-emitting semiconductor lasers with polarization-selected optical feedback

We study experimentally and numerically the dynamic states of chaotic oscillations in vertical-cavity surface-emitting semiconductor lasers (VCSELs) with polarization-selected optical feedback. We identify the regimes of fully-developed chaotic states, low-frequency fluctuations (LFFs), and coexistent states of LFFs and stable oscillation for the variations of the bias injection current and the optical feedback ratio. In particular, coexistent states of LFFs and stable oscillations are observed at higher optical feedback ratio and lower bias injection current. We draw maps of dynamic states in the space of the bias injection current and the optical feedback ratio. The qualitative agreement between the theory and the experiment is found.     

Controlling chaos in RCL-shunted Josephson junction by delayed linear feedback

The resistively-capacitively-inductively-shunted （RCL-shunted） Josephson junction （RCLSJJ） shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.     

Controlling chaos in RCL-shunted Josephson junction by delayed linear feedback

The resistively--capacitively--inductively-shunted (RCL-shunted) Josephson junction (RCLSJJ) shows chaotic behaviour under some parameter conditions. Here a scheme for controlling chaos in the RCLSJJ is presented based on the linear feedback theory. Numerical simulations show that this scheme can be effectively used to control chaotic states in this junction into stable periodic states. Moreover, the different stable period states with different period numbers can be obtained by appropriately adjusting the feedback intensity and delay time without any pre-knowledge of this system required.     

耦合反馈控制双环掺铒光纤激光器混沌

 提出双环掺铒光纤激光器耦合反馈控制混沌的物理模型,利用定向耦合器将系统的输出变量反馈到系统中,通过间接控制损耗系数,并选取适当的反馈系数,实现对系统混沌的控制。分析了反馈系数对激光器由混沌态进入周期态和稳定态的动力学行为的影响。数值模拟表明：改变系统损耗系数,双环掺铒光纤激光器可由周期态进入混沌态;加入耦合反馈,适当调制反馈系数,可以将双环光纤激光器混沌控制到周期态和稳定态上;提高系统反馈系数,系统进入稳定态的时间变短。选取不同的系统初值,激光器总能得到两种不同的奇怪吸引子,可见双环掺铒光纤激光器具有双稳态特征。     

混沌神经网络的延时反馈控制研究

针对混沌神经网络，提出了一种改进的延时反馈控制方法. 利用该方法，当延时参数τ为奇数时，被控神经网络收敛于记忆模式以及它的反相模式的2周期上. 若选取不同的延时参数，被控网络则收敛于不同的周期态上. 关键词： 控制混沌 延时反馈控制 混沌神经网络     

Bifurcation,chaotic phenomena and control of chaos in a one—dimensional discrete Josephson lattice

We have investigated the fluxon dynamical behaviour in a one-dimensional parallel array of small Josephson junctions in the presence of an externally applied magnetic field. In the case of high damping,the system is in stable state. On the contrary, in the case of low damping, bifurcation and chaotic phenomena have been observed. Control of chaos is achieved by a delayed feedback mechanism, which drives the chaotic system into a selected unstable periodic orbit embadded within the associated strange attractor. It is attractive to control chaos to a periodic state, rather than operating always outside the device parameter space where chaos dominates.     

Non-stationary characteristics of instability in a single-mode Nd:YVO 4 laser with fiber feedback

Random chaotic burst generation was experimentally observed in a single-mode microchip Nd:YVO₄ laser with fiber feedback. As the feedback strength was increased, a transition from stable relaxation oscillation state to unstable random chaotic burst state appeared. Furthermore, the non-stationary characteristic of probability association was experimentally identified at the transition of the two states while similar characteristics were reported only by numerical simulations of simple dynamical systems. This implies the general feature of non-stationary property of the dynamic switching between two states at transition. The observed chaotic burst generation and non-stationary nature were reproduced numerically based on the Lang-Kobayashi model. Received 28 March 2001 and Received in final form 5 June 2001     

Controlling Chaotic Behavior in a Bose-Einstein Condensate with Linear Feedback

The spatial structure of a Bose-Einstein condensate (BEC) loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative.     

Photonic integrated device for chaos applications in communications

A novel photonic monolithic integrated device consisting of a distributed feedback laser, a passive resonator, and active elements that control the optical feedback properties has been designed, fabricated, and evaluated as a compact potential chaotic emitter in optical communications. Under diverse operating parameters, the device behaves in different modes providing stable solutions, periodic states, and broadband chaotic dynamics. Chaos data analysis is performed in order to quantify the complexity and chaoticity of the experimental reconstructed attractors by applying nonlinear noise filtering.     

Chaotifying a stable linear controllable system by single input state feedback

In this paper, an approach for chaotifying a stable controllable linear system via single input state-feedback is presented. The overflow function of the system states is designed as the feedback controller, which can make the fixed point of the closed-loop system to be a snap-back repeller, thereby yields chaotic dynamics. Based on the Marotto theorem, it proves theoretically that the closed-loop system is chaotic in the sense of Li and Yorke. Finally, the simulation results are used to illustrate the effectiveness of the proposed method.     

延时线性反馈法控制双环掺铒光纤激光器混沌

根据线性反馈法控制混沌的理论及实践成果,提出了延时线性反馈法控制双环掺铒光纤激光器混沌的具体方案.计算机模拟结果表明,适当调节反馈系数和延时时间,可以实现对双环掺铒光纤激光器混沌的稳定控制 关键词： 混沌控制 延时线性反馈 双环掺铒光纤激光器     

Extensive chaos in the Lorenz-96 model

We explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by Lorenz to study fundamental issues regarding the forecasting of spatially extended chaotic systems such as the atmosphere. First, we explore the spatiotemporal chaos limit by increasing the system size while holding the magnitude of the external forcing constant. Second, we explore the strong driving limit by increasing the external forcing while holding the system size fixed. As the system size is increased for small values of the forcing we find dynamical states that alternate between periodic and chaotic dynamics. The windows of chaos are extensive, on average, with relative deviations from extensivity on the order of 20%. For intermediate values of the forcing we find chaotic dynamics for all system sizes past a critical value. The fractal dimension exhibits a maximum deviation from extensivity on the order of 5% for small changes in system size and the deviation from extensivity decreases nonmonotonically with increasing system size. The length scale describing the deviations from extensivity is consistent with the natural chaotic length scale in support of the suggestion that deviations from extensivity are due to the addition of chaotic degrees of freedom as the system size is increased. We find that each wavelength of the deviation from extensive chaos contains on the order of two chaotic degrees of freedom. As the forcing is increased, at constant system size, the dimension density grows monotonically and saturates at a value less than unity. We use this to quantify the decreasing size of chaotic degrees of freedom with increased forcing which we compare with spatial features of the patterns.     

光电反馈混沌系统脉冲同步特性研究

提出光电反馈混沌状态下的混沌脉冲同步.首先, 对激光器的混沌动力学方程进行了数值分析, 通过改变反馈系数和脉冲系数来观测混沌状态的变化, 实现了对混沌激光器的控制;然后, 对脉冲同步方程进行数值分析, 给出了同步的模拟图.实验结果表明此方法能实现混沌同步.     

Design of output feedback controller for a unified chaotic system

In this paper, the synchronization of a unified chaotic system is investigated by the use of output feedback controllers; a two-input single-output feedback controller and single-input single-output feedback controller are presented to synchronize the unified chaotic system when the states are not all measurable. Compared with the existing results, the controllers designed in this paper have some advantages such as small feedback gain, simple structure and less conservation. Finally, numerical simulations results are provided to demonstrate the validity and effectiveness of the proposed method.     

Forcing and control of localized states in optical single feedback systems

Under feedback extended nonlinear optical systems spontaneously show a variety of periodic patterns and structures. Control gives new insight into these phenomena and it can open the way for potential application of nonlinear optical structures. We briefly review methods to control localized states in single feedback experiments. Application of a Fourier control method allows to modify interaction behavior of the localized states. As a further approach we study a forcing method, using externally created light fields as additional input to the system. Recent experiments show that the forcing method enables to favor addressing positions for localized structures. We demonstrate static addressing and favoring of addressing positions. We extend the forcing method to a dynamic forcing scheme, which allows to move and reposition localized states. Additionally forcing is used to balance experimental imperfections. PACS 05.45.Gg; 42.60.Jf; 42.65.Tg     

Design of output feedback controller for a unified chaotic system

In this paper, the synchronization of a unified chaotic system is investigated by the use of output feedback controllers; a two-input single-output feedback controller and single-input single-output feedback controller are presented to synchronize the unified chaotic system when the states are not all measurable. Compared with the existing results, the controllers designed in this paper have some advantages such as small feedback gain, simple structure and less conservation. Finally, numerical simulations results are provided to demonstrate the validity and effectiveness of the proposed method.     

Theory of stability and bifurcation in a multi-quantum well laser with opto-electronic delayed feedback

This paper presents an opto-electronic feedback multi-quantum well laser system and outlines our study of the dynamics and bifurcation in a multi-quantum well laser due to the opto-electronic delayed feedback effect. We point out theoretically the conditions of stability and Hopf bifurcation of the laser. The relaxation oscillation frequency of the system is educed to be the function of the feedback level, delayed time and in-current. The route from stability to bifurcation is numerically simulated via varying the delayed time, feedback strength and in-current. The results show that the induced dynamics can be grouped into four distinct types or modes (stable, periodic pulsed, undamped oscillating or beating, and chaos), where the frequency and intensity varying with the delayed time in the two periodic regions are analyzed detailedly to find that the pulsing frequency is reduced with the long delayed time while the pulsing intensity is added with the long delayed time. And the chaotic pulsing frequency is increased with the large in-current. In addition, the carrier transport between the barrier region and the active region can characterize the dynamics in the laser to produce stable, periodic pulsed, beating and chaotic states by altering the carriers transport or escape rate value.     

利用锯齿非线性混沌化稳定的Takagi-Sugeno (TS) 模糊系统

研究了利用任意小幅值的状态反馈控制来混沌化稳定的Takagi-Sugeno (TS) 模糊系统问题。所用状态反馈控制器是系统状态的锯齿函数。我们应用改进的Marotto定理从数学上证明了受控系统在Li-Yorke意义下是混沌的。特别地，给出了计算混沌化参数的解析公式。最后一个数值例子被用来说明所提的理论结果。     

Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering

Experiments on chaotically oscillating arrays of 64 nickel electrodes in sulfuric acid were carried out. External resistors in parallel and series are added to vary the extent of global coupling among the oscillators without changing the other properties of the system. The array is heterogeneous due to small variations in the properties of the electrodes and there is also a small amount of noise. The addition of global coupling transforms a system of independent elements to a state of complete synchronization. At intermediate coupling strengths stable clusters, or condensates of elements, form. All the elements in a cluster follow the same chaotic trajectory but each cluster has its own dynamics; the system is thus temporally chaotic but spatially ordered. Many cluster configurations occur under the same conditions and transitions among them can be produced. For values of the coupling parameter on either side of the stable cluster region a non-stationary behavior occurs in which clustered and synchronized states alternately form and break up. Some statistical properties of the cluster states are determined. (c) 2000 American Institute of Physics.