Interaction between oscillations in a self-stochastic system

A system of two bistable circuits connected by a low-pass filter is studied theoretically and experimentally. It is demonstrated that the system may produce self-excited chaotic oscillations. To examine the interaction between respective chaotic oscillations in bistable circuits, motion equations are derived and a numerical analysis of the interaction is carried out. Results of an experiment on a breadboard model are presented.     

Chaotic oscillations in a coupled system of bistable oscillators

The influence of the asymmetry of the nonlinear element characteristic on the chaotic oscillations of Chua’s bistable oscillator is studied. It is shown that such asymmetry causes asymmetry of a chaotic attractor that maps the switching of motions between two basins of attraction up to the concentration of oscillations in one basin. Oscillation control in a bistable chaotic self-oscillating system (two coupled Chua’s oscillators) is considered. It is demonstrated that oscillations excited in two basins of attraction may pass to one of them and that oscillations may build up in two basins when they are autonomously excited in different basins. It is also found that chaotic oscillations in a coupled system may be excited at parameter values for which the autonomous chaotic oscillations of partial oscillators are absent. The influence of external noiselike oscillations is investigated.     

Chaos synchronization with signal distortion in a communication channel: Experiment and numerical simulation

The effect of filtering properties of a communication channel on dynamic regulations and synchronization of oscillations in a system of two unidirectionally coupled generators of chaotic signals is studied in natural radiophysics and numerical experiments. The amplitude and phase relations between the signals of the trailing and leading systems are studied for varying transmission band of the filter and the extent of signal attenuation in the communication channel. The results of measurements are confirmed by calculations of the coherence function and variance of the phase difference of oscillations.     

Stabilization of unstable fixed points in the dynamics of a laser with feedback

We report theoretical and experimental results on the stabilization of unstable steady states in a CO2 laser with feedback. Periodic and chaotic oscillations have been suppressed by means of a control loop consisting of a high-pass filter, known as washout filter. Although the filter characteristics are determined on the basis of linear analysis, taking into account the problem of robustness with respect to parameter changes, the present control strategy provides a large attractive domain in the phase space.     

Self-sustained oscillations in systems with delay under irregularly varying excitation conditions

A mathematical model of a system consisting of two coupled chaotic delay subsystems is presented. Instead of constant initial conditions in the form of a single impetus to excite the subsystems, continuous irregular oscillations are used that simulate intrinsic noise and continue acting on self-sustained oscillations after their excitation. An equation of an autonomous subsystem with regard to feedback variation is derived. It is shown that, when an autonomous subsystem is excited by irregular oscillations, chaotic motions become stochastic. In this case, the intensity of oscillations simulating intrinsic noise increases, suppressing self-sustained oscillations and providing the regenerative amplification of irregular oscillations. Interaction of coupled oscillations for identical and nonidentical subsystems is considered for the case of different noiselike initial conditions. It is found that interacting oscillations are not completely identical even if the parameters of the subsystems are the same.     

Nonlinear dynamics of an optical phase locked loop in presence of additional loop time delay

The dynamics of an optical phase locked loop (OPLL) with first order loop filter having inherent loop time delay is investigated. In the presence of delay, the system is modeled as a third order autonomous system. In the out of lock condition or during the process of locking, the dynamics of the system is highly nonlinear and different nonlinear phenomena, like limit cycle oscillation, period doubling, chaotic oscillations etc., may be observed with the variation of design parameters. Applying the techniques of the nonlinear dynamics, we have calculated the effects of the inherent loop time delay in determining the state of the loop. The analytical results predicting the parameter values for stable and unstable region of operation are obtained using the quasi-linear Routh–Hurwitz method. The parameter range required for the onset of chaotic oscillations is estimated by Melnikov's global perturbation method. The predicted results are in agreement with those obtained by numerical integration of system equations.     

Hysteresis-induced bifurcation and chaos in a magneto-rheological suspension system under external excitation

The magneto-rheological damper(MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom(2-DOF) MR suspension system was established first, by employing the modified Bouc–Wen force–velocity(F –v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface.The largest Lyapunov exponent(LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density(PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy(K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system.     

Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlinear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester(MOA) is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as period doubling bifurcation(PDB), saddle node bifurcation(SNB), Hopf bifurcation(HB), and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.     

Mutual synchronization in a system of two bistable oscillators executing regular and chaotic oscillations

A numerical analysis of a new model describing two coupled modified Chua??s oscillators is conducted. Equations of a partial oscillator differ from classical equations in that the former contain additional delayed feedback in another writing of dimensionless time. Changeover from regular oscillations in the absence of additional feedback to additional-feedback-induced (switchable) chaotic oscillations is studied. It is shown that, when normal regular oscillations, as well as additional-feedback-induced chaotic oscillations, are synchronized, difference oscillations are left. They are absent only when the control parameters of partial oscillators are identical. The application of a harmonic signal allows one to control the oscillations of a chaotic system of coupled modified bistable oscillators.     

Noise-induced chaos in non-linear dynamics of El Niños

Motivated by an important practical significance, we analyze the noise-induced El Niño evolutionary equations. Our analysis based on the evaluation of largest Lyapunov exponents demonstrates the new effects of deterministic and stochastic dynamics of the El Niño–Southern Oscillation Events. We show that the non-linear deterministic model possesses either a multiturn limit cycle with regular self-oscillations or chaotic oscillations depending on slight variations of one of the main system parameters – the mean tropical easterlies. It is revealed that in the presence of noise, transformations of regular oscillations into chaotic ones are observed.     

用多凹槽滤波器控制混沌系统

提出了一种施加多个凹槽滤波器反馈控制混沌系统的方法,使混沌运动转化为规则的运动.多凹槽滤波器控制是一种具有固定参数的线性反馈控制方法,它不影响原系统的参数,截断了系统从倍周期分叉通向混沌的道路.同时,用Melnikov方法进行理论分析,给出了合适的反馈控制器的参数.将多凹槽滤波器应用于典型的混沌系统,其仿真结果表明了该控制方法的有效性与可行性 关键词： 混沌 多凹槽滤波器 Melnikov方法     

Periodic window arising in the parameter space of an impact oscillator

In the bi-dimensional parameter space of an impact-pair system, shrimp-shaped periodic windows are embedded in chaotic regions. We show that a weak periodic forcing generates new periodic windows near the unperturbed one with its shape and periodicity. Thus, the new periodic windows are parameter range extensions for which the controlled periodic oscillations substitute the chaotic oscillations. We identify periodic and chaotic attractors by their largest Lyapunov exponents.     

混沌信号自适应协同滤波去噪

混沌信号协同滤波去噪算法充分利用了混沌信号的自相似结构特征,具有良好的信噪比提升性能.针对该算法的滤波参数优化问题,考虑到最优滤波参数的选取受到信号特征、采样频率和噪声水平的影响,为提高该算法的自适应性使其更符合实际应用需求,基于排列熵提出一种滤波参数自动优化准则.依据不同噪声水平的混沌信号排列熵的不同,首先选取不同滤波参数对含噪混沌信号进行去噪,然后计算各滤波参数对应重构信号的排列熵,最后通过比较各重构信号的排列熵,选取排列熵最小的重构信号对应的滤波参数为最优滤波参数,实现滤波参数的优化.分析了不同信号特征、采样频率和噪声水平情况下滤波参数的选取规律.仿真结果表明,该参数优化准则能在不同条件下对滤波参数进行有效的自动最优化,提高了混沌信号协同滤波去噪算法的自适应性.     

Spike-burst synchronization in an ensemble of electrically coupled discrete model neurons

In this paper, we study the dynamics of a system of two model neurons interacting via the electrical synapse. Each neuron is described by a two-dimensional discontinuous map. A chaotic relaxational-type attractor, which corresponds to the spiking-bursting chaotic oscillations of neurons is shown to exist in a four-dimensional phase space. It is found that the dynamical mechanism of formation of chaotic bursts is based on a new phenomenon of generation of transient chaotic oscillations. It is demonstrated that transition from the chaotic-burst generation to the state of relative rest occurs with a certain time delay. A new characteristic which estimates the degree of synchronization of the spiking-bursting oscillations is introduced. The dependence of the synchronization degree on the strength of coupling of the ensemble elements is studied.     

Transition between synchronization and chaos in doped GaAs/AlAs superlattices

The transition between chaotic and periodic regimes in spontaneous current oscillations of weakly coupled, doped GaAs/AlAs superlattices has been observed by varying the external d.c. bias. The chaotic current oscillations are observed for voltage ranges, which exhibit a large negative differential conductance in the time-averaged I–V characteristic. Since this system can be described by a spatially distributed, non-linear system with many degrees of freedom, the coupling between the degrees of freedom in the chaotic windows is repulsive, while in the periodic windows it is attractive.     

混沌系统的遗传神经网络控制

提出遗传神经网络控制混沌新方法.将小扰动技术和周期控制技术结合起来，用遗传算法训练神经网络，使之成为混沌控制器.对Henon映射和Logistic映射的仿真结果说明控制器能产生小扰动控制序列信号，将混沌振荡转变成规则运动状态.该方法无需了解动态系统数学模型，具有一定抗噪声干扰能力，可将它推广应用到其他混沌系统的控制中. 关键词： 遗传算法 神经网络 混沌 周期控制     

一种基于三阶Volterra滤波器的混沌时间序列自适应预测方法

基于Takens的相空间延迟坐标重构,研究了用于混沌信号预测的三阶Volterra滤波器的一种乘积耦合近似实现结构,并应用于典型的低维混沌时间序列和具有高维混沌特性的EEG信号的预测.数值研究表明:这种滤波器结构对于低维混沌时间序列的预测精度可以比二阶Volterra滤波器提高103倍,而且能够较好地对一些具有高维混沌特性的EEG信号进行预测 关键词： 混沌 非线性自适应预测 三阶Volterra滤波器 electroencephalography信号     

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.     

用数字有限脉冲响应滤波器控制混沌

利用数字有限脉冲响应滤波器稳定微分动力系统和二维离散映象混沌吸引子中不稳定周期轨道的方法，实现了高周期轨道的稳定控制.分别研究了Lorenz系统和Henon映象，给出了初步的分析和数值模拟结果.这种方法的主要特点是不需要获取混沌系统中不稳定周期轨道的任何信息，控制参数的选择与被控混沌系统无关. 关键词：     

基于复合非线性数字滤波器的Hash函数构造

在对多个满足Kelber条件的滤波器组成的复合系统进行初步分析的基础上，提出了一个基于复合非线性数字滤波器的带密钥的Hash算法.算法首先构建能产生高维混沌序列的复合滤波器系统，然后在明文作用的复合序列控制下随机选择滤波器子系统，并以复合系统的初态作为密钥，以粗粒化的量化迭代轨迹作为明文的Hash值.讨论了复合系统实现Hash函数的不可逆性、防伪造性、初值敏感性等特点.研究结果表明：基于复合非线性数字滤波器的Hash算法简单快速，比基于单一混沌映射的Hash算法有着更高的安全性，同时滤波器结构中没有复杂的浮点运算，比一般复合混沌系统更易于软硬件实现. 关键词： Hash 函数 混沌 非线性自回归数字滤波器