A METHOD FOR CALCULATING THE LYAPUNOV EXPONENT SPECTRUM OF A PERIODICALLY EXCITED NON-AUTONOMOUS DYNAMICAL SYSTEM

The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimension D-L((A)) of the autonomous system, the definition of the Lyapunov dimension D-L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely, D-L((A)) - D-L = 1. For a quasi-periodically excited dynamical system, similar conclusions are formed.

Modeling Dynamical Noises Corrupted Chaotic System for Heart Rate Variability Analysis

It is difficult to establish the process of chaos in time series from cardiac dynamics. The output from such a system is probably the result of both its internal dynamics, and the input to the system from its surroundings. We present an optimization algorithm to find a time series that is as close as possible to the heart rate series subject to the constraint that it is deterministic with respect to some dynamics. The algorithm is tested by some famous forced dynamical systems, and applied to heart rate data. We find that the deterministic components of heart rate variability are chaotic.

Decrease in Hurst exponent of human gait with aging and neurodegenerative diseases

In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range （R/S） analysis method. It indicates that the long-range correlations of gait rhythm from young healthy people are stronger than those from the healthy elderly and the diseased. The result further implies that fractal dynamics in human gait will be altered due to weakening or impairment of neural control on locomotion resulting from aging and neurodegenerative diseases. Due to analysing short-term data sequences rather than long datasets required by most nonlinear methods, the algorithm has the characteristics of simplicity and sensitivity, most importantly, fast calculation as well as powerful anti-noise capacities. These findings have implications for modelling locomotor control and also for quantifying gait dynamics in varying physiologic and pathologic states.

Detecting dynamical complexity changes in time series using the base-scale entropy

Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series： the base-scale entropy. The definition directly applies to arbitrary real-word data. We illustrate our method on a practical speech signal and in a theoretical chaotic system. The results show that the simple and easily calculated measure of base-scale entropy can be effectively used to detect qualitative and quantitative dynamical changes.

Investigation of the Quaternion Dynamical System

The quaternion Mandelbrot set is one of the most important sets in mathematics. In this paper we first give some properties of the quaternion algebra. Then, we introduce the quternion dynamical system. We are concerned with analytical and numerical investigation of the quaternion dynamical system.

Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems

We propose a clustering-based approach for identifying coherent flow structuresin continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then cluster these data from differentinitial locations into groups. The method then uses the normalized standarddeviation or mean absolute deviation to quantify the deformation. Unlike the usualfinite-time Lyapunov exponent (FTLE), the proposed algorithm considers the completetraveling history of the particles. We also suggest two extensions of the method. To improvethe computational efficiency, we develop an adaptive approach that constructsdifferent subsamples of the whole particle trajectory based on a finite time interval. Tostart the computation in parallel to the flow trajectory data collection, we also developan on-the-fly approach to improve the solution as we continue to provide more measurementsfor the algorithm. The method can efficiently compute the WCVE over adifferent time interval by modifying the available data points.

NMR relaxation and diffusion studies to probe the motional dynamics of risperidone within PLGA microsphere

The present study aims to investigate the motional dynamics of risperidone within polylactic co-glycolic acid(PLGA)microsphere by employing solution state'H and 19F nuclear magnetic resonance(NMR)measurements.Risperidone,a second-generation fluorinated antipsychotic drug used for the treatment of schizophrenia is commercially marketed as PLGA microsphere formulation resulting in prolonged release of the drug in solution.Although the current trend in the pharmaceutical market is to develop drug formulation with long-acting release(LAR)products,complete physicochemical characterization of such formulations are scarce.Especially the effects of microsphere encapsulation on the motional properties and diffusion behavior of the drugs are not discussed adequately in any of the earlier reports.We therefore,have employed NMR relaxation and diffusion measurements to decipher the interaction of PLGA cavity water with risperidone.A detailed analysis of NMR relaxation rates confirmed the event of encapsulation and the presence of local motion in the non-fluorinated end of risperidone.Further,the relaxation data indicated a significant alteration in 19F chemical shift anisotropy(CSA)and CSA/dipole-dipole(DD)cross-correlated relaxation mechanism and decreased effect of solvent relaxation pointing out reduced water concentration within the microsphere cavity.'H and 19F diffusion coefficients of risperidone led to the information about hydrodynamic radius of risperidone in free and encapsulated states.Measurement of hydrodynamic radius supported the presence of limited water in PLGA cavity allowing higher translational mobility of risperidone after the encapsulation.

圆弧足被动行走机器人动力学参数影响研究

被动行走机器人运动特性主要取决于动力学参数的选择。为研究参数变化对机器人步态的影响,以圆弧足被动行走机器人为研究对象,利用拉格朗日方法建立动力学方程并进行了数值仿真。借助分岔理论研究了圆弧足半径、质心位置、转动惯量和斜坡倾角对机器人稳定步态的影响。采用正交扰动向量法求解被动行走机器人这种非光滑系统的李雅普诺夫指数,对分岔动力学进行了验证。结果表明:随着质心位置、转动惯量和斜坡倾角增大,机器人步态出现倍周期分岔现象,当圆弧足半径在特定区间内增大时机器人仍保持周期一步态,但足半径过度增大会导致步态失稳;另外,双参数研究中对圆弧足半径和质心位置联合作用下机器人稳定参数区间变化进行了分析,并且发现机器人步态呈现出逆倍周期分岔现象。该研究结果为未来双足步行机器人的优化设计和主动控制提供了重要参考。

平行轴涡动黏性充液转子动力稳定性计算和影响因素分析

超重力离心机转子系统在临界转速之上存在液-固耦合激振诱发的失稳区域,该失稳区域的存在直接威胁充液类超重力离心机转子的安全稳定运行,同时严重制约了离心机转子向高转速、大型化方向发展.本研究旨在探究充液离心机转子的液-固耦合机理及减振措施,通过建立黏性充液转子的流体动力学方程,结合连续性方程以及边界条件并耦合转子的动力学方程,开展超重力充液类离心机转子的动力稳定性的计算方法研究.首先,推导扰动形式的纳维-斯托克斯方程,采用有限差分的数值计算手段求解上述扰动形式的流体动力学方程,得到壁面处的流体压强与流体剪切力并进行数值积分;其次,将所求液体等效主刚度系数及交叉刚度系数与转子动力学方程进行耦合,并采用状态空间法降阶求解动力学方程的阻尼衰减指数和涡动频率.经过对比充液转子系统在变转速区间内的阻尼衰减指数变化瀑布图与交叉刚度变化瀑布图,发现充液转子的稳定性是转子系统的阻尼、刚度、充液比和流体黏性等多个特性参数作用的结果,具体表现为增加转子系统外阻尼以及降低系统交叉刚度对抑制转子失稳与振动具有明显效果.

Influence of temperature, stress, and grain size on behavior of nano-polycrystalline niobium

Atomic simulations are executed to investigate the creep responses of nano-polycrystalline(NC) niobium established by using the Voronoi algorithm. The effects of varying temperature, applied stress, and grain size(GS) on creep properties and mechanisms are investigated. Notably, the occurrence of tertiary creep is exclusively observed under conditions where the applied stress exceeds 4.5 GPa and the temperature is higher than 1100 K. This phenomenon can be attributed to the significant acceleration of grain boundary and lattice diffusion, driven by the elevated temperature and stress levels. It is found that the strain rate increases with both temperature and stress increasing. However, an interesting trend is observed in which the strain rate decreases as the grain size increases. The stress and temperature are crucial parameters governing the creep behavior. As these factors intensify, the creep mechanism undergoes a sequential transformation: initially from lattice diffusion under low stress and temperature conditions to a mixed mode combining grain boundaries(GBs) and lattice diffusion at moderate stress and mid temperature levels, and ultimately leading to the failure of power-law controlled creep behavior, inclusive of grain boundary recrystallization under high stress and temperature conditions. This comprehensive analysis provides in more detail an understanding of the intricate creep behavior of nano-polycrystalline niobium and its dependence on various physical parameters.

Dynamics Modeling and Stability Analysis of Tilt Wing Unmanned Aerial Vehicle During Transition

In the transition mode of quad tilt wing-unmanned aerial vehicle(QTW-UAV),the system stability of UAV will change with the tilt angle changes,which will cause serious head drop down.Meanwhile,with the complex air flow and other disturbances,the system is prone to side bias,frying,stall and other kinetic stability problems,hence the system stability analysis has become an urgent problem to be solved.To solve the stability problem,we need the quantitative criteria of system stability and effective tool of stability analysis,and can improve the stability of the motion control by optimizing the structural parameters of the aircraft.Therefore,based on the design of the mechanical structure,the quantitative relationship between the structure parameters of the aerial vehicle and kinetic stability of the system transition mode is established by the Lyapunov exponent method.In this paper,the dynamic modeling of the position and attitude angle is carried out and the stability of the system is analyzed by Lyapunov exponent,the results show that changing the mechanical structure of the system can improve the flight stability for the system transition mode and lay a theoretical foundation for the system stability analysis.Compared with the Lyapunov direct method,this method can be construct easily,has a simple calculation process and so on.We improve the flight stability by optimizing the structure and the experiment confirms that expanding area can enhance flight stability within limits.

Nonlinear Dynamic Analysis of the Whole Vehicle on Bumpy Road

Through the research into the characteristics of 7-DoF high dimensional nonlinear dynamics of a vehicle on bumpy road, the periodic movement and chaotic behavior of the vehicle were found.The methods of nonlinear frequency response analysis, global bifurcation, frequency chart and Poincaré maps were used simultaneously to derive strange super chaotic attractor.According to Lyapunov exponents calculated by Gram-Schmidt method, the unstable region was compartmentalized and the super chaotic characteristic of ...

DYNAMIC STRAIN AGING BEHAVIOR OF K40S ALLOY

The dynamic strain aging behavior during tensile tests of K40S alloy has been investigated in the temperature range of 25-1100℃ with the strain rate range from 10-4 to 10-3s-1. The results show that four different types of serration, identified as A, B, C and E type serration were observed in the temperature range of 300-600℃. The strain exponents for onset of the serrated flow were calculated as 1.21, 2.19 and 1.61, and the activation energies as 121, 40 and 67kJ/mol for E, B and C type serration respectively. The main mechanism for dynamic strain aging discussed in light of the strain exponent and the activation energy.

Nonlinear Dynamic Analysis of MPEG-4 Video Traffic

The main research motive is to analysis and to veiny the inherent nonlinear character of MPEG-4 video. The power spectral density estimation of the video trafiic describes its 1/f^β and periodic characteristics.The priraeipal compohems analysis of the reconstructed space dimension shows only several principal components can be the representation of all dimensions. The correlation dimension analysis proves its fractal characteristic. To accurately compute the largest Lyapunov exponent, the video traffic is divided into many parts.So the largest Lyapunov exponent spectrum is separately calculated using the small data sets method. The largest Lyapunov exponent spectrum shows there exists abundant nonlinear chaos in MPEG-4 video traffic. The conclusion can be made that MPEG-4 video traffic have complex nonlinear be havior and can be characterized by its power spectral density,principal components, correlation dimension and the largest Lyapunov exponent besides its common statistics.

Short-Time Dynamics of the Random n-Vector Model

Short-time critical behavior of the random n-vector model is studied by the theoretic renormalization-group approach.Asymptotic scaling laws are studied in a frame of the expansion in e = 4 - d for n ≠ 1 and for n = 1respectively.In d ＜ 4,the initial slip exponents θ′ for the order parameter and θ for the response function are calculated up to the second order in e ＝ 4 - d for n ≠ 1 and for n ＝ 1 at the random fixed point respectively.Our results show that the random impurities exert a strong influence on the short-time dynamics for d ＜ 4 and n ＜ nc.

不同缓冲(能力)跑鞋对跑者膝、踝关节局部动态稳定性的影响

目的:通过最大Lyapunov指数评价局部动态稳定性,探究传统、极简和极致缓震3类跑鞋(后跟高度分别为33、8、46 mm,掌跟差分别为12、0、10 mm)对跑步过程中膝、踝关节动态稳定性影响的差异,为跑者鞋具选择提供建议。方法:采用惯性测量单位传感器比较跑者[年龄:(26.3±1.1)岁,身高:(1.75±0.02)m,体质量:(63.3±2.7)kg,BMI:(20.8±1.3)kg/m^(2))]以(10.8±0.5)km/h的速度在跑步机上持续跑步时下肢关节峰值合加速度,通过Rosenstein算法计算最大Lyapunov指数,评估3类跑鞋在跑步过程中对下肢局部动态稳定性的影响。采用单因素方差分析对数据进行统计学分析,采用Tukey HSD事后多重检验进行组间比较,显著性水平设置为P<0.05。结果:1)跑者穿着传统跑鞋的峰值合加速度大于极致缓震跑鞋,但小于极简跑鞋,且所有组间两两比较结果均具有显著差异(P<0.01);2)跑者穿着3类跑鞋的踝关节合加速度的最大Lyapunov指数具有显著差异(P=0.018),相比极简跑鞋,跑者着极致缓震跑鞋的踝关节合加速度的最大Lyapunov指数显著增大(均值差=0.13,P=0.014);3)跑者膝关节合加速度的最大Lyapunov指数变化显著(P<0.01),相比极简跑鞋[(0.652±0.20)bits/s],跑者穿着传统跑鞋[(0.937±0.15)bits/s,P=0.0003]和极致缓震跑鞋[(0.936±0.12)bits/s,P=0.0003]的膝关节合加速度的最大Lyapunov指数显著增大。结论:1)从下肢关节峰值加速度角度,极致缓震跑鞋较传统跑鞋和极简跑鞋具有更好的缓冲减震作用,着地时的胫骨峰值加速度更小;2)从局部动态稳定性角度,极简跑鞋较传统跑鞋和极致缓震跑鞋在跑步的过程中具有更好的下肢局部动态稳定性,系统减弱外部干扰的能力更好,说明穿着极简跑鞋跑步时的步态更自然;3)传统跑鞋由于产生的下肢关节峰值加速度相对较小且具有较好的局部动态稳定性,对于注重兼顾跑步时的缓冲减震以及动态稳定性作用的跑者是更优的选择。

Analyzing vegetation dynamic trend on the Mongolian Plateau based on the Hurst exponent and influencing factors from 1982–2013

This study analyzed the spatial and temporal variations in the Normalized Difference Vegetation Index(NDVI) on the Mongolian Plateau from 1982–2013 using Global Inventory Modeling and Mapping Studies(GIMMS) NDVI3 g data and explored the effects of climate factors and human activities on vegetation. The results indicate that NDVI has slight upward trend in the Mongolian Plateau over the last 32 years. The area in which NDVI increased was much larger than that in which it decreased. Increased NDVI was primarily distributed in the southern part of the plateau, especially in the agro-pastoral ecotone of Inner Mongolia. Improvement in the vegetative cover is predicted for a larger area compared to that in which degradation is predicted based on Hurst exponent analysis. The NDVI-indicated vegetation growth in the Mongolian Plateau is a combined result of climate variations and human activities. Specifically, the precipitation has been the dominant factor and the recent human effort in protecting the ecological environments has left readily detectable imprints in the NDVI data series.

非线性动力系统在分岔点处的临界慢化行为

Lyapunov指数是定量描述非线性动力系统轨道稳定性的主要方法之一,同时也是分析系统分岔行为的常用手段.实际应用中,人们通常只关心Lyapunov指数的正负,并以此来判断系统轨道是否稳定,而对于Lyapunov指数为零,即动力学分岔点处系统的行为特征讨论甚少.本文以几类经典的非线性动力系统为例,针对系统在分岔点处的轨道稳定性进行理论和数值分析.研究发现,不同系统在分岔点处其微扰后的轨道均以幂律,而非指数的形式收敛,呈现出经典物理系统在相变临界点处的慢化行为.通过理论分析,我们解析得到分岔点处计算临界指数的一般公式,并通过数值模拟对理论公式的准确性进行了验证.临界慢化是物理系统在相变点处的普遍现象,文中关于非线性系统在分岔点处临界慢化行为的发现将加深人们对于动力学分岔本质的认识,同时也是对现有教材中关于Lyapunov指数相关知识的有益补充.

基于动态Hurst指数的人脑老化复杂度分析

目的研究健康成人在不同年龄段的功能特点可以更好地理解人脑的老化过程,Hurst指数可以测量静息态功能磁共振成像时间序列的复杂度。既往对大脑复杂度随年龄变化的研究,还存在样本量小、未考虑复杂度的动态变化等局限性。因而有必要在大样本被试上通过刻画复杂度的动态变化特性,来研究人脑随年龄变化的规律。方法选择19~80岁的458名健康成人静息态功能磁共振成像数据,划分为青年组(n=213)、中年组(n=142)和老年组(n=103),通过滑窗法来计算动态Hurst指数,并进一步提取其平均值、标准差和变异系数特征来描述人脑的动态复杂度水平和波动程度,最后通过统计分析来评判不同年龄组被试的复杂度差异。结果在平均值特征上,双侧颞上回、双侧岛回、右侧扣带回和双侧腹中侧枕叶皮层的复杂度随年龄增长而降低,而双侧眶回和左侧楔前叶的复杂度则随年龄的增长而呈现出倒U形变化;在标准差和变异系数特征上,老年组在右侧楔前叶的动态复杂度显著大于青年组和中年组。结论人脑老化过程中全脑复杂度动态变化模式并不一致,且在不同的年龄段上,局部脑区存在不同的组间统计显著差异模式。该结果可以为研究者理解正常老化的功能机制提供帮助。

Nonlinear dynamics investigation of contact force in a cam–follower system using the Lyapunov exponent parameter,power spectrum analysis,and Poincarémaps

The aim of this article is to detect the detachment between the cam and the follower using the largest Lyapunov exponent parameter,the power density function of fast Fourier transform,and Poinarémaps due to the nonlinear dynamics phenomenon of the follower.The detachment between the cam and the follower was investigated for different cam speeds and different internal distances of the follower guide from inside.This study focuses on the use of the cam–follower system with a bionic quadruped robot through a linkage mechanism.Multishock absorber(spring–damper–mass)systems at the very end of the follower were used to improve the dynamic performance and to reduce the detachment between the cam and the follower.The SolidWorks program was used in the numerical solution,while a high‐speed camera at the foreground of the OPTOTRAK 30/20 equipment was used to identify the follower position.The friction and impact were considered between the cam and the follower and between the follower and its guide.In general,when the cam and the follower are in permanent contact,there is no loss in potential energy,and no impact or restitution.The detachment between the cam and the follower increases with increasing coefficient of restitution in the presence of the impact.