Chaos in Acoustic Subspace Raised by the Sommerfeld–Kononenko Effect

This paper deals with vibrations of an infinite plate in contact with an acoustic medium where the plate is subjected to a point excitation by an electric motor of limited power-supply. The whole system is divided into two “exciter - foundation” and “foundation-plate-medium”. In the system “motor-foundation” three classes of steady state regimes are determined: stationary, periodic and chaotic. The vibrations of the plate and the pressure in the acoustic fluid are described for each of these regimes of excitation. For the first class they are periodic functions of time, for the second they are modulated periodic functions, in general with an infinite number of carrying frequencies, the difference between which is constant. For the last class they correspond to chaotic functions. In another mathematical model where the exciter stands directly on an infinite plate (without foundation) it was shown that chaos might occur in the system due to the feedback influence of waves in the infinite hydro-elastic subsystem in the regime of motor shaft rotation. In this case the process of rotation can be approximately described as a solution of the fourth order nonlinear differential equation and may have the same three classes of steady state regimes as the first model. That is the electric motor may generate periodic acoustic waves, modulated waves with an infinite number of frequencies or chaotic acoustic waves in a fluid.     

Chaotic dynamics in a neural network under electromagnetic radiation

In this paper, a small Hopfield neural network with three neurons is studied, in which one of the three neurons is considered to be exposed to electromagnetic radiation. The effect of electromagnetic radiation is modeled and considered as magnetic flux across membrane of the neuron, which contributes to the formation of membrane potential, and a feedback with a memristive type is used to describe coupling between magnetic flux and membrane potential. With the electromagnetic radiation being considered, the previous steady neural network can present abundant chaotic dynamics. It is found that hidden attractors can be observed in the neural network under different conditions. Moreover, periodic motion and chaotic motion appear intermittently with variations in some system parameters. Particularly, coexistence of periodic attractor, quasiperiodic attractor, and chaotic strange attractor, coexistence of bifurcation modes and transient chaos can be observed. In addition, an electric circuit of the neural network is implemented in Pspice, and the experimental results agree well with the numerical ones.     

Analysis and applied study of dynamic characteristics of chaotic repeller in complicated system

Introduction Inrecentyears,thestudyondynamicbehaviorofnonlinearsystemhasbecomeanactive subjectinnonlinearscience[1-12].Chaosisakindofcomplicatedandirregularbehaviorcseated bynonlinearsystem,suchirregularphenomenonexistsinnatureandsocietywidely.Itiswell_ known,timeserieswithcomplicatedphenomenonandbehaviorincludingchaosexistinvarious complicatedsystemsandinengineeringtechniques,suchsituationsareusuallytreatedeffectively withchaotictheoriesandmethods.Uptonowseveralmaturedstatisticindexesformeasu…     

Novel techniques for improving NNetEn entropy calculation for short and noisy time series

Entropy is a fundamental concept in the field of information theory. During measurement, conventional entropy measures are susceptible to length and amplitude changes in time series. A new entropy metric, neural network entropy (NNetEn), has been developed to overcome these limitations. NNetEn entropy is computed using a modified LogNNet neural network classification model. The algorithm contains a reservoir matrix of N = 19,625 elements that must be filled with the given data. A substantial number of practical time series have fewer elements than 19,625. The contribution of this paper is threefold. Firstly, this work investigates different methods of filling the reservoir with time series (signal) elements. The reservoir filling method determines the accuracy of the entropy estimation by convolution of the study time series and LogNNet test data. The present study proposes 6 methods for filling the reservoir for time series of any length 5 ≤ N ≤ 19,625. Two of them (Method 3 and Method 6) employ the novel approach of stretching the time series to create intermediate elements that complement it, but do not change its dynamics. The most reliable methods for short-time series are Method 3 and Method 5. The second part of the study examines the influence of noise and constant bias on entropy values. In addition to external noise, the hyperparameter (bias) used in entropy calculation also plays a critical role. Our study examines three different time series data types (chaotic, periodic, and binary) with different dynamic properties, Signal-to-Noise Ratio (SNR), and offsets. The NNetEn entropy calculation errors are less than 10% when SNR is greater than 30 dB, and entropy decreases with an increase in the bias component. The third part of the article analyzes real-time biosignal EEG data collected from emotion recognition experiments. The NNetEn measures show robustness under low-amplitude noise using various filters. Thus, NNetEn measures entropy effectively when applied to real-world environments with ambient noise, white noise, and 1/f noise.

     

基于LSTM模型的飞行器智能制导技术研究

人工智能技术的突破性进展为飞行器再入制导技术的研究提供了新的技术途径, 本文针对预测校正制导中两方面的问题: 一是纵向“预测环节”积分计算量大和“校正环节”割线法迭代求解难以满足实时性的问题, 二是纵向制导和横向制导都需要对动力学方程进行积分, 存在明显的冗余计算问题, 提出基于长短期记忆网络(long short-term memory, LSTM) 的飞行器智能制导技术. 一方面, 在纵向制导中不需要对动力学方程进行积分来预测待飞射程, 即去除“预测环节”; 另一方面, 不再基于割线法迭代求解倾侧角的幅值, 即去除倾侧角的“校正环节”, 大大减少积分计算量, 提高计算速度. 利用深度学习在神经网络映射能力和实时性方面的双重天然优势, 基于再入飞行器的实时状态信息, 采用LSTM模型实时生成倾侧角指令. 同时, 将纵向和横向制导环节的制导周期统一为一个周期, 进一步确保制导系统满足在线制导的实时性要求. 蒙特·卡罗仿真分析表明, 本文所提的方法在飞行器再入初始状态和气动参数拉偏情况下具有精度和速度上的优势.      

卷积神经网络在流场重构研究中的进展

近年来, 随着深度学习在图像处理、语音识别、自动驾驶、自然语言处理等领域迅速发展, 该技术也被越来越广泛地应用于处理具有复杂非线性、高维度、大数据量等特点的流体力学方向. 传统的方法无法有效地处理这些庞大的数据, 深度学习因其具有强大的函数拟合能力, 可以从大量的数据中挖掘有用的信息. 当前, 流体力学深度学习技术有了初步的一些研究成果, 在流动信息特征提取、多源数据信息融合及流场的智能重构等方面具有重要的工程价值, 其应用潜力逐渐得到证实. 如何利用地面风洞试验、数值模拟及飞行试验获取的数据进行深入挖掘, 快速智能感知及重构流场, 可为主动流动控制提供重要指导. 本文主要从深度学习不同类型的网络结构出发探讨了卷积神经网络在流场重构中的研究进展, 文章首先介绍卷积神经网络的一些基本概念以及基本网络结构, 之后简要介绍流场超分辨率重构网络、端到端的映射网络、长短期记忆网络的基本结构与理论, 并详细归纳出他们的改进形式在流场重构领域的一系列研究进展与成果, 最后对文章做出总结并探讨了流场重构深度学习技术所面临的挑战与展望.      

Detecting unstable periodic orbits and unstable quasiperiodic orbits in vibro-impact systems

In this paper, unstable dynamics is considered for the models of vibro-impact systems with linear differential equations coupled to an impact map. To provide a skeleton for the organization of chaotic attractors, we propose a method for detecting unstable periodic orbits embedded in chaotic attractors through a combination of unconstrained optimization technique and Poincaré map. Three numerical examples from different vibro-impact models demonstrate that the strategy can efficiently detect unstable periodic orbits in chaotic attractors. In order to explore the mechanism responsible for the creation of multi-dimensional tori attractors, we also present another method to detect unstable quasiperiodic orbits embedded multi-dimensional tori attractors by examining a specially transient time series. The upper bound and lower bound of the transient time series (in the Poincaré map) can be obtained by analyzing transient Lyapunov exponent and transient Lyapunov dimension. Some examples verify the effectiveness of the numerical algorithm.     

Existence and stability analysis of bifurcating periodic solutions in a delayed five-neuron BAM neural network model

In this paper, a bidirectional associative memory (BAM) neural network model, which consists of two neurons in the X-layer and three neurons in the Y-layer, with two time delays, will be considered. By analyzing the associated characteristic equation, we obtain that Hopf bifurcation occurs and a family of periodic solutions appears. Moreover, the stability and the period of the bifurcating periodic solutions are studied. To illustrate our theoretical results, numerical simulations are presented.     

STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES＊

The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural networks and wavelet theories, the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given. Based on wavelet networks, a new method for parameter identification was suggested, which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series. Through pre-treatment and comparison of results before and after the treatment, several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.     

Modeling and prediction of chaotic systems with artificial neural networks

This study of chaotic systems and their prediction is motivated by the fact that many phenomena, both natural and man‐made, are of a chaotic nature. Such phenomena include but are not limited to earthquakes, laser systems, epileptic seizures, combustion, and weather patterns. These phenomena have previously been thought to be unpredictable. However, it is indeed possible to predict time series generated by chaotic systems. The primary objective of this study is to develop a system that would train the artificial neural network (ANN) and then predict the future data of the process. In the present application, the chosen chaotic data set was obtained by solving Lorenz's equations. To predict the future data, the concept of a multilayer feed‐forward ANN with nonlinear auto‐regressive moving averages with exogenous input is used. A Backpropagation algorithm is used to train the network for the chaotic data. The final updated weights from the trained network were then used for the prediction of the future values of the system. Lyapunov exponents, phase diagrams and statistical analyses were used to evaluate the neural network output. A correlation of 94% and a negative Lyapunov exponent indicate that the results obtained from ANN are in good agreement with the actual values. Copyright © 2009 John Wiley & Sons, Ltd.     

Bifurcation,periodic and chaotic motions of the modified equal width-Burgers (MEW-Burgers) equation with external periodic perturbation

The modified equal width-Burgers (MEW-Burgers) equation is introduced for the first time. The bifurcation behavior of the MEW-Burgers equation is studied. Considering an external periodic perturbation, the periodic and chaotic motions of the perturbed MEW-Burgers equation are investigated by using phase projection analysis, time series analysis, Poincaré section and bifurcation diagram. The strength (\(f_0\)) of the external periodic perturbation plays a crucial role in the periodic and chaotic motions of the perturbed MEW-Burgers equation.     

混沌时间序列预测的局域法在边坡变形分析中的应用

边坡作为一个复杂系统,其本身的各种参量是不确定的和随机的,在其演化过程中,表现出复杂的非线性行为,发生一系列的混沌现象。本文运用现代混沌理论,对边坡变形的预测问题进行探索性研究,把混沌时间序列理论引入到边坡工程研究中,对该理论的建立及预测方法进行系统地讨论,为该领域的研究提供完整的技术方法。通过对新滩滑坡的研究结果表明,混沌时间序列方法对混沌序列的预测较线性时间序列具有较高的精度。     

STUDY ON THE PREDICTION METHOD OF LOW_DIMENSION TIME SERIES THAT ARISE FROM THE INTRINSIC NONLINEAR DYNAMIC

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PREDICTION TECHNIQUES OF CHAOTIC TIME SERIES AND ITS APPLICATIONS AT LOW NOISE LEVEL

The paper not only studies the noise reduction methods of chaotic time series with noise and its reconstruction techniques,but also discusses prediction techniques of chaotic time series and its applications based on chaotic data noise reduction.In the paper,we first decompose the phase space of chaotic time series to range space and null noise space.Secondly we restructure original chaotic time series in range space.Lastly on the basis of the above,we establish order of the nonlinear model and make use of the nonlinear model to predict some research.The result indicates that the nonlinear model has very strong ability of approximation function,and Chaos predict method has certain tutorial significance to the practical problems.     

Nonlinear dynamics of self-, parametric,and externally excited oscillator with time delay: van der Pol versus Rayleigh models

The regular and chaotic vibrations of a nonlinear structure subjected to self-, parametric, and external excitations acting simultaneously are analysed in this study. Moreover, a time delay input is added to the model to control the system response. The frequency-locking phenomenon and transition to quasi-periodic oscillations via Hopf bifurcation of the second kind (Neimark–Sacker bifurcation) are determined analytically by the multiple time scales method up to the second-order perturbation. Approximate solutions of the quasi-periodic motion are determined by a second application of the multiple time scales method for the slow flow, and then, slow–slow motion is obtained. The similarities and differences between the van der Pol and Rayleigh models are demonstrated for regular, periodic, and quasi-periodic oscillations, as well as for chaotic oscillations. The control of the structural response, and modifications of the resonance curves and bifurcation points by the time delay signal are presented for selected cases.

     

Rich dynamics caused by diffusion

It is an awfully difficult task to design an efficient numerical method for bifurcation diagrams, the graphs of Lyapunov exponents, or the topological entropy about discrete dynamical systems by linear/nonlinear diffusion with the Direchlet/Neumann- boundary conditions. Until now there are less works concerned with such a problem. In this paper, we propose a scheme about bifurcating analysis in a series of discrete-time dynamical systems with linear/nonlinear diffusion terms under the periodic boundary conditions. The complexity of dynamical behaviors caused by the diffusion term are to be determined. Bifurcation diagrams are shown by numerical simulation and chaotic behavior (chaotic Turing patterns) is demonstrated by computing the largest Lyapunov exponent. Our theoretical model can give an interesting case study about the phenomenon: the individuals exhibit a very simple dynamics but the groups with linear/nonlinear coupling can own a complex dynamics including fluctuation, periodicity and even chaotic behavior. We find that diffusion can trigger chaotic behavior in the present system and there exist multiple Turing patterns. It is interesting as regular or chaotic patterns can be reported in this study. Chaotic orbits emerge when exploring further in the diffusion coefficient space, and such a behavior is entirely absent in the corresponding continuous time-space system. The method proposed in the present paper is innovative and the conclusion is novel.

     

Modeling Human Chaotic Behavior: Nonlinear Forecasting Analysis of Logistic Iteration

Does the unpredictability of human behavior arise from randomness, from deterministic but chaotic processes, or from humans' use of (possibly nonlinear deterministic) heuristics in coping with complicated situations? One way to find out might be to see whether humans can behave chaotically when asked to do so. Previous work showed that when humans are asked to generate a series of numbers according to a particular chaotic equation they can do so but not in exactly the way the equation would generate them. Nonetheless, their series of guesses do contain nonlinear deterministic structure, which is one indication that they may be generated by a chaotic process. Series of guesses generated by a computer simulation of a model that simulates the heuristic thought processes of the humans making the guesses also contain nonlinear deterministic structure of the same order as the logistic the humans are attempting to mimic. Thus, when faced with a chaotic process, humans seem to cope by using a heuristic process that approximates the chaotic process within the limitations of human memory and performance.     

Study on the Prediction Method of Low-Dimension Time Series that Arise from the Intrinsic Nonlinear Dynamics

The prediction methods and its applications of the nonlinear dynamic systems determined from chaotic time series of low-dimension are discussed mainly. Based on the work of the foreign researchers, the chaotic time series in the phase space adopting one kind of nonlinear chaotic model were reconstructed. At first, the model parameters were estimated by using the improved least square method. Then as the precision was satisfied, the optimization method was used to estimate these parameters. At the end by using the obtained chaotic model, the future data of the chaotic time series in the phase space was predicted. Some representative experimental examples were analyzed to testify the models and the algorithms developed in this paper. The results show that if the algorithms developed here are adopted, the parameters of the corresponding chaotic model will be easily calculated well and true. Predictions of chaotic series in phase space make the traditional methods change from outer iteration to interpolations. And if the optimal model rank is chosen, the prediction precision will increase notably. Long term superior predictability of nonlinear chaotic models is proved to be irrational and unreasonable. Paper from Chen Yu-shu, Member of Editorial of Committee, AMM Foundation item: the National Natural Science Foundation of China (19990510); the National Key Basic Research Special Fund(G1998020316) Biography: Ma Jun-hai(1965-), Professor, Doctor     

A comparison of different approaches to detect the transitions from regular to chaotic motions in SMA oscillator

Meccanica - It is well known that dynamical systems that include devices based on shape memory alloys (SMA) can exhibit a wide spectrum of responses: periodic, quasi-periodic and chaotic motions....