CHAOS, CHAOS CONTROL AND SYNCHRONIZATION OF ELECTRO-MECHANICAL GYROSTAT SYSTEM

The dynamic behavior of electro-mechanical gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, Period-T maps, and Lyapunov exponents are presented to observe periodic and chaotic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. Several methods, the delayed feedback control, adaptive control algorithm (ACA) control are used to control chaos effectively. Anticontrol of chaos destroyed the periodic motions and replaced by chaotic motion effectively by adding constant motor torque and adding periodic motor torque. Finally, synchronization of chaos in the electro-mechanical gyrostat system is studied.     

基于参数切换算法的混沌系统吸引子近似及其电路设计

基于参数切换算法和离散混沌系统, 设计一种新的混沌系统参数切换算法, 给出了两算法的原理. 采用混沌吸引子相图观测法, 研究了不同算法下统一混沌系统和Rössler混沌系统参数切换结果, 最后引入方波发生器, 设计了Rössler混沌系统参数切换电路. 结果表明, 采用参数切换算法可以近似出指定参数下的系统, 其吸引子与该参数下吸引子一致; 基于离散系统的参数切换结果更为复杂, 当离散序列分布均匀时, 只可近似得到指定参数下的系统; 相比传统切换混沌电路, 参数切换电路不用修改原有系统电路结构, 设计更为简单, 输出结果受方波频率影响, 通过加入合适频率的方波发生器, 数值仿真与电路仿真结果一致.     

CHAOS AND CHAOS SYNCHRONIZATION OF A SYMMETRIC GYRO WITH LINEAR-PLUS-CUBIC DAMPING

The dynamic behavior of a symmetric gyro with linear-plus-cubic damping, which is subjected to a harmonic excitation, is studied in this paper. The Liapunov direct method has been used to obtain the sufficient conditions of the stability of the equilibrium points of the system. By applying numerical results, time history, phase diagrams, Poincaré maps, Liapunov exponents and Liapunov dimensions are presented to observe periodic and chaotic motions. Besides, several control methods, the delayed feedback control, the addition of constant motor torque, the addition of period force, and adaptive control algorithm (ACA), have been used to control chaos effectively. Finally, attention is shifted to the synchronization of chaos in the two identical chaotic motions of symmetric gyros. The results show that one can make two identical chaotic systems to synchronize through applying four different kinds of one-way coupling. Furthermore, the synchronization time is also examined.     

Exponential sine chaotification model for enhancing chaos and its hardware implementation

Chaotic systems have been intensively studied for their roles in many applications, such as cryptography, secure communications, nonlinear controls, etc. However, the limited complexity of existing chaotic systems weakens chaos-based practical applications. Designing chaotic maps with high complexity is attractive. This paper proposes the exponential sine chaotification model (ESCM), a method of using the exponential sine function as a nonlinear transform model, to enhance the complexity of chaotic maps. To verify the performance of the ESCM, we firstly demonstrated it through theoretical analysis. Then, to exhibit the high efficiency and usability of ESCM, we applied ESCM to one-dimensional (1D) and multi-dimensional (MD) chaotic systems. The effects were examined by the Lyapunov exponent and it was found that enhanced chaotic maps have much more complicated dynamic behaviors compared to their originals. To validate the simplicity of ESCM in hardware implementation, we simulated three enhanced chaotic maps using a digital signal processor (DSP). To explore the ESCM in practical application, we applied ESCM to image encryption. The results verified that the ESCM can make previous chaos maps competitive for usage in image encryption.     

Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincar\'{e} maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.     

A robust steganographic technique based on improved chaotic-range systems

This paper presents a novel chaos-based technique of steganography in spatial domain. In the last decade, chaos theory has gained utmost importance in multimedia security applications. Generally, 1-D chaotic maps are employed because of computational ease and structural simplicity but their limited chaotic range is an obstacle. In the proposed work, we model the nonlinear combinations of 1-D chaotic maps. These chaotic systems possess chaotic behavior throughout the domain. We, for the first time, propose an effective application of these improved chaotic systems in steganography. These newly synthesized systems are used to embed secret information in the least significant bits (LSBs) of the host image. By comparing with some recent models, we prove that involving improved chaotic systems in steganographic approach really produces extraordinary outcomes. We determine the strength of our steganographic algorithm through the most significant statistical analyses such as information entropy, correlation, contrast, energy, homogeneity, peak signal to noise ratio (PSNR) and mean square error (MSE). We further prove the robustness of the anticipated technique against several image processing attacks. The upshot of these analysis techniques shows that our algorithm is highly reliable and produces coherent results.     

Suppression of chaos and other dynamical transitions induced by intercellular coupling in a model for cyclic AMP signaling in Dictyostelium cells

The effect of intercellular coupling on the switching between periodic behavior and chaos is investigated in a model for cAMP oscillations in Dictyostelium cells. We first analyze the dynamic behavior of a homogeneous cell population which is governed by a three-variable differential system for which bifurcation diagrams are obtained as a function of two control parameters. We then consider the mixing of two populations behaving in a chaotic and periodic manner, respectively. Cells are coupled through the sharing of a common chemical intermediate, extracellular cAMP, which controls its production and release by the cells into the extracellular medium; the dynamics of the mixed suspension is governed by a five-variable differential system. When the two cell populations differ by the value of a single parameter which measures the activity of the enzyme that degrades extracellular cAMP, the bifurcation diagram established for the three-variable homogeneous population can be used to predict the dynamic behavior of the mixed suspension. The analysis shows that a small proportion of periodic cells can suppress chaos in the mixed suspension. Such a fragility of chaos originates from the relative smallness of the domain of aperiodic oscillations in parameter space. The bifurcation diagram is used to obtain the minimum fraction of periodic cells suppressing chaos. These results are related to the suppression of chaos by the small-amplitude periodic forcing of a strange attractor. Numerical simulations further show how the coupling of periodic cells with chaotic cells can produce chaos, bursting, simple periodic oscillations, or a stable steady state; the coupling between two populations at steady state can produce similar modes of dynamic behavior.     

Non-linear dynamics and control of chaos for a rotational machine with a hexagonal centrifugal governor with a spring

The dynamic behaviors of the rotational machine with a hexagonal centrifugal governor which is subjected to external disturbance are studied in the paper. The Lyapunov direct method is applied to obtain conditions of stability of the equilibrium points of system. By applying numerical results, phase diagrams, power spectrum, Poincaré maps, and Lyapunov exponents are presented to observe periodic and chaotic motions. The effect of the parameter changes in the system can be found in the bifurcation and parametric diagrams. Finally, eight methods are used to control chaos effectively.     

基于现场可编程门阵列技术的混沌数字通信系统——设计与实现

提出了基于IEEE-754标准和现场可编程门阵列(FPGA)技术的混沌数字通信系统的通用设计与硬件实现的一种新方法,实现了混沌加密体制与传统密码体制的结合.根据Euler算法,对连续混沌系统作离散化处理,通过FPGA硬件设计混沌离散系统,使其产生作为密钥的混沌数字序列,其中加密算法采用置乱扩展技术,并对算法进行了分析.设计驱动响应式同步保密通信系统,构建包含信号在内的闭环,实现发送端与接收端离散混沌系统的同步.以网格蔡氏混沌系统为例,对该保密通信系统进行了FPGA硬件实验,给出了技术实现过程、算法流程、硬 关键词： 网格多涡卷蔡氏电路 置乱扩展矩阵 现场可编程门阵列技术 混沌数字通信系统     

一种混沌映射的相空间去噪方法

对于混沌映射来说,它们的频谱比混沌流的频谱更广阔,与噪声频谱的重叠率更高,所以混沌流的去噪方法对它们并不适用. 在半盲分析法的框架下,混沌系统的参数估计问题终将归结为最小二乘估计问题. 本文从最小二乘拟合的角度出发估计混沌映射的演化参数,进而通过相空间重构以及投影操作,实现对观测信号的噪声抑制. 实验结果表明,该算法的去噪效果优于扩展卡尔曼滤波器（extended Kalman filter,EKF）和无先导卡尔曼滤波器（unscneted Kalman filter,UKF）,并且能够较大程度地将信号源的混沌特征量还原. 关键词： 混沌 噪声抑制 相空间重构 投影     

Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order

The dynamical behaviour of the generalized Korteweg-de Vries (KdV) equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincaré maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.     

Self-emergence of chaos in the identification of irregular periodic behavior

Various forms of chaotic synchronization have been proposed as ways of realizing associative memories and/or pattern recognizers. To exploit this kind of synchronization phenomena in temporal pattern recognition, a chaotic dynamical system representing the class of signals that are to be recognized must be established. This system can be determined by means of identification techniques. The fulfillment of the chaotic condition could be imposed as a constraint. However, it is shown here that, even for a very simple identification algorithm, chaos emerges by itself, allowing us to model the diversity of nearly periodic signals.     

Dynamical chaos for a limited power supply for fluid oscillations in cylindrical tanks

Forced oscillations of the fluid surface in a cylindrical tank due to interaction with the excitation mechanism of a limited power supply (so-called “limited excitation” phenomena) are investigated in detail. On the basis of analysis of the largest Lyapunov exponents for a complex system—a tank with fluid and an excitation arrangement—the three types of steady-state regimes are found: equilibrium positions, periodic and chaotic regimes. Phase portraits, Poincaré sections and maps, distributions of spectral densities and invariant measures are constructed and thoroughly studied. Attention is concentrated mainly on the properties of chaotic attractors and schemes of transition from “order” to chaos. It is established that different scenarios of transition to chaos and various structures of chaotic attractors are possible in the same physical system. The new scenario transition to chaos which generalizes scenario of Pomeau-Manneville is revealed. It is shown that chaotic regimes with the single-mode fluid free surface oscillations can originate only due to interaction with the excitation mechanism.     

Multiple period-doubling bifurcation route to chaos in periodically pulsed Murali-Lakshmanan-Chua circuit-controlling and synchronization of chaos

We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system.     

Spread-spectrum communication using binary spatiotemporal chaotic codes

We propose a scheme to generate binary code for baseband spread-spectrum communication by using a chain of coupled chaotic maps. We compare the performances of this type of spatiotemporal chaotic code with those of a conventional code used frequently in digital communication, the Gold code, and demonstrate that our code is comparable or even superior to the Gold code in several key aspects: security, bit error rate, code generation speed, and the number of possible code sequences. As the field of communicating with chaos faces doubts in terms of performance comparison with conventional digital communication schemes, our work gives a clear message that communicating with chaos can be advantageous and it deserves further attention from the nonlinear science community.     

CHAOS, CHAOS CONTROL AND SYNCHRONIZATION OF A GYROSTAT SYSTEM

The dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and choatic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Several methods, the delayed feedback control, the addition of constant torque, the addition of periodic force, the addition of periodic impulse torque, injection of dither signal control, adaptive control algorithm (ACA) control and bang-bang control are used to control chaos effectively. Finally, synchronization of chaos in the gyrostat system is studied.     

频率扫描法研究倍周期分岔与混沌现象

在一类非线性系统中,应用频率控制方法,对倍周期分岔与混沌行为进行了研究。在V₀-ω外控参数平面上,频率扫描显示了分岔与混沌的整体结构:正的和逆的倍周期分岔序列的对称性;分岔收敛于一点的封闭性。本文中所建议的方法,将是一种研究分岔与混沌现象有效而快速的手段。它不仅能定量测量收敛比δ和标度因子α,分段展开还能定性地观察阵发混沌和嵌套在混沌带中的各种窗口等。分岔与混沌是一类非线性系统的频率响应。 关键词：     

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.     

Order patterns and chaos

Chaotic maps can mimic random behavior in a quite impressive way. In particular, those possessing a generating partition can produce any symbolic sequence by properly choosing the initial state. We study in this Letter the ability of chaotic maps to generate order patterns and come to the conclusion that their performance in this respect falls short of expectations. This result reveals some basic limitation of a deterministic dynamic as compared to a random one. This being the case, we propose a non-statistical test based on ‘forbidden’ order patterns to discriminate chaotic from truly random time series with, in principle, arbitrarily high probability. Some relations with discrete chaos and chaotic cryptography are also discussed.