Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.

Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system

A new method is presented to generate two-directional (2D) grid multi-scroll chaotic attractors via a specific form of the sine function and sign function series, which are applied to increase saddle points of index 2. The scroll number in the x-direction is modified easily through changing the thresholds of the specific form of the sine function, while the scroll number in the y-direction is controlled by the sign function series. Some basic dynamical properties, such as equilibrium points, bifurcation diagram, phase portraits, and Lyapunov exponents spectrum are studied. Furthermore, the electronic circuit of the system is designed and its simulation results are given by Multisim 10.

基于改进Jerk模型的跳跃滑翔目标跟踪

针对雷达对跳跃滑翔目标跟踪问题,提出了一种基于改进Jerk模型的无迹卡尔曼滤波(UKF)跟踪算法。该方法针对常规Jerk算法需要人为预先设定加加速度方差和“急动”频率而引入的估计误差,通过当前位置估计值和当前位置一步预测值进行加加速度方差自适应计算,并将“急动”频率与加加速度方差相关联,在目标运动状态估计的同时实现了模型参数自适应调整。同时,将改进Jerk模型与UKF算法相结合,给出了整体算法流程,并进行了仿真实验。仿真结果表明,与常规Jerk模型算法相比,本文提出的方法实现了模型参数的自适应调整,在跟踪过程中更能适应目标的机动特性。

Jerk曲线连续的改进S型加减速算法研究

高精度的运动平台中,冲击是影响运动平台运动精度以及平稳性的重要因素。针对传统S型加减速算法所存在的Jerk曲线存在突变的问题,提出了一种Jerk曲线光滑的高平稳改进S型加减速算法。首先,以具有高柔性的正弦函数为基础,构造Jerk曲线;其次,为了克服嵌入式系统中计算正弦函数困难的问题,应用切夫雪比多项式逼近正弦函数,获得完整的加减速控制算法。在此基础上,进一步推导得出不同条件下各个阶段具体的时间规划;最后,在MATLAB环境中,进行仿真实验。实验结果表明,改进加减速算法的Jerk曲线连续且光滑,可实现不同初始参数下的平稳运行,提高了运动平台的控制精度。

The study of geomagnetic jerk from 2010 to 2021 based on hourly mean data from global geomagnetic observatories

The secular variation in the global geomagnetic field was analyzed in terms of the annual differences in monthly means by using the hourly mean data from 18 foreign(outside China)observatories of the World Data Center(WDC)for Geomagnetism from January 2010 to January 2020 as well as 9 observatories in the Geomagnetic Network of China from January 2015 to April 2021.In addition,according to the correlation of noisy components from the observatories,a covariance matrix was constructed based on residuals between observations and the CHAOS-7.4 model to remove external contamination.Through a comparison before and after denoising,we found that the overall average standard deviations were reduced by 29.97%in China and by 41.4%outside China.Results showed the correlation coefficient between external noise(mainly the magnetosphere ring current)and the Dst index was 0.82,and the correlation coefficient between external noise and the Ring Current(RC)index reached 0.94.A geomagnetic jerk was globally discovered around 2018.0 on the geomagnetic eastward component Y.The jerk timing in China was around 2020.0,and the earliest one was in2018.75,whereas the timing outside China was around 2018.0,and the earliest one was in 2017.67.This 2-year lag may have been caused by the higher electrical conductivity of the deep mantle.After more data were added,this jerk event was found to occur in an orderly manner in the northern hemisphere as the longitude increased and the intensity gradually increased as well.The variations in location of the jerk center were analyzed according to the CHAOS-7.4 model.Results revealed six extreme points distributed nearby the equator.The strongest was near the equator,at 170°E,and the strength gradually decreased as it extended to the northern and southern hemispheres.Another extreme point with the opposite sign was located at the equator,at 20°W,in the south-central part of the Atlantic,and the strength gradually decreased as it extended into Europe.The covariance matrix method can be used to analyze data from the Macao Science Satellite-1 mission in the future,and this method is expected to play a positive role in modeling and separating the large-scale external field.

An Atomic Product: The Unison Jerk in Drug Transportation

A three dimensional unison product with third derivative of displacement system of differential equations is presented. A projected plasma efavirenz concentration profile of a patient who had been on an orally administered 600 mg daily dose of efavirenz is used as a structural aggregate. A three compartmental model of ordinary differential equations is suggested and solved numerically. The model projects descriptors associated with the product of a bounce that is a closed system. The product consists of three independent phases with two variable states, intenseness (concentration) that measures a structural aggregate and an environmental influence which is gravity. The third phase of the product is a processing function (spartial aggregate) which is a free potential. The function, a free potential, is responsible for ordering the product. A dynamical system with an attractive subspace which is an external potential (stable) with a zero eigenvalue is derived. The unison jerk’s Jacobian Matrix has corresponding negative, positive and zero eigenvalues.

一种基于忆阻的退化Jerk系统的混沌动力学分析

将双曲余弦忆阻器模型引入退化Jerk系统,设计了一个新的忆阻混沌系统。利用数值仿真对系统进行研究,通过相图、分岔图、Lyapunov指数谱等分析了系统的动力学行为。新系统不仅存在依赖于忆阻初始条件变化的无限多共存吸引子的多稳定现象,还存在依赖于系统参数变化的周期极限环和混沌吸引子。最后在Simulink结果中观测到与数值仿真一致的结果,证明了系统的存在性和可实现性。

多涡卷Jerk混沌吸引子及其实现

以多涡卷Jerk系统为例,介绍了利用DSP处理器实现连续混沌系统的方法。同时设计了相应的模拟硬件电路,并分别给出了硬件实验结果。实验结果表明,利用DSP产生的实验结果与模拟电路产生的结果完全一致,证实了该方法的可行性。该方法同样可以实现其他连续混沌系统,具有普适性。该方法还存在着调试方便,参数调节灵活,计算误差可控性强,频谱调节范围较宽且方便等优点,便于实现数字保密通信。

一种新型的Jerk连续加减速控制方法研究

传统数控加工中加减速控制采用直线加减速方法和指数加减速方法但加速度都存在突变,使机床产生柔性冲击,现国内外一些先进的CNC系统采用S形曲线加减速方法,但S曲线实际上可看作是分段的多项式形式,其加加速度是分段恒定的,存在的不连续点使加加速度在某时刻突变,仍会导致机床整个运动中存在冲击和振动。为此提出一种基于加加速度控制的加减速控制方法,采用限制加加速值,并利用滤波器对加速度进行光滑处理来减少加工中由于加加速突变而产生的机床振动,进而实现高表面质量加工,同时又能达到机床良好的加减速性能。

一种高度机动目标的“当前”统计Jerk模型

讨论了KishoreMehrotra等提出的高度机动目标模型———Jerk模型 ,应用古典控制论方法分析了该模型的局限性 ;提出了一种新的“当前”统计Jerk模型 ,即CS Jerk模型 ,该模型假设目标的机动加速度变化率为非零均值指数相关的随机过程 ;仿真结果表明CS

机动目标跟踪α-jerk模型

本文针对jerk模型中人为设定参数α值的不合理性,对机动时间常数的倒数α进行建模,提出新的α-jerk模型,并给出相应的α-jerk滤波算法。该模型在估计目标状态的同时,能够实时估计参数α的值。仿真结果表明α-jerk模型比jerk模型收敛速度更快,状态估计更精确。

高度机动目标的改进CS-Jerk模型

针对高度机动目标跟踪问题,通过对Jerk模型的分析,借鉴"当前"统计的思想,采用截断正态分布来表征目标机动加速度变化率(Jerk)特性,利用Jerk均值与方差之间的关系自适应调整过程噪声协方差矩阵,提出一种改进的"当前"统计Jerk模型(MCS-Jerk model);并通过理论分析指出了Jerk模型及其跟踪算法的缺陷以及改进的MCS-Jerk模型算法的有效性;仿真结果表明改进的模型及跟踪算法的高机动目标跟踪性能明显优于基于Jerk模型的跟踪算法。

高度机动目标Jerk模型及改进算法

针对Jerk模型常规算法跟踪Jerk机动时存在稳态确定性误差的固有缺陷,提出了Jerk模型改进算法。改进算法融合了Jerk模型及当前Jerk模型。Jerk模型描述弱Jerk机动,采用位置估计偏差和加速度变化率方差之间的关系调整系统噪声方差;当前Jerk模型描述强Jerk机动,采用修正瑞利分布描述加速度变化率方差统计特性。在滤波算法方面,引入模糊分布函数和强跟踪滤波器,改善了对弱Jerk机动的跟踪精度,并提高了对强Jerk机动的跟踪能力。理论分析和仿真结果表明,改进算法克服了Jerk模型常规算法的缺陷,能自适应地逼近不同强度的Jerk机动并进行准确跟踪。该算法在不同强度信号噪声比和不同量测噪声下,误差变化相对稳定,具有较好的跟踪精度。

多涡卷jerk电路混沌系统的分析与滑模控制

针对多涡卷jerk电路混沌系统,讨论了系统的基本动力行为;运用非线性系统理论和Routh-Hurwitz定理分别对系统平衡点的稳定性作了分析,得到了相关的定理,作出了系统的分叉图。同时对系统的追踪控制问题,采用滑模控制方法,有效地实现了多涡卷混沌系统对给定参考信号的追踪控制。最后通过数值示例进行仿真,对文中论述进行了论证。

高度机动目标的“当前”统计Jerk模型

讨论了KishoreMehrotra等人提出的高度机动目标模型———Jerk模型 ,得出了该模型在跟踪阶跃Jerk信号时存在确定性稳态误差的结论。提出了一种新的“当前”统计Jerk(currentstatisticJerk ,CS -Jerk)模型 ,该模型假设目标的机动加速度变化率为非零均值指数相关的随机过程。仿真结果表明 ,CS -Jerk模型及其滤波算法在跟踪高度机动目标时性能优于Jerk模型。

一种Jerk连续的正弦函数平方曲线加减速算法研究

针对传统直线加减速和指数加减速算法在进给过程中具有柔性冲击,特别是S曲线加减速存在加加速度不连续问题,提出了一种位移、速度、加速度、Jerk都连续的正弦函数平方曲线加减速算法。通过仿真实验结果表明,正弦函数平方曲线加减速算法是一种具有Jerk连续的新型柔性加减速方法。

多级修正的高机动Jerk模型研究

基于Jerk模型及当前统计模型,提出了一种多级修正的高机动Jerk模型(MJerk).在假设机动加速度变化率(即加加速度)为非0均值指数相关随机过程的条件下,通过对Jerk模型状态分量作Taylor级数展开,得到了各状态分量的Jerk修正方程,使得机动加加速度对系统各状态分量的作用得到反映,减小了模型误差.Monte Carlo数值仿真表明,在进行高机动目标跟踪时,MJerk模型的均方根误差比Jerk模型的约减小了20%,而二者的计算量相当.

具有隐藏吸引子的三维Jerk系统的动力学分析与周期解

数值分析了一类具隐藏吸引子的三维Jerk系统在不同参数条件下的周期1、周期2、混沌吸引子、Lyapunov指数谱、分叉等,并运用Poincare紧致化理论对系统的无穷远动力学进行了分析,通过零倾线给出了系统在无穷远点处的局部动力学行为.同时,运用平均化方法和等时系统扰动理论,定性分析并计算了系统的解析周期解.最后通过数值实验,对平均化方法所得解析周期解与Rong-Kutta方法所得数值解进行了仿真,验证了文中理论分析的正确性.

应用优化的同伦分析法求解非线性Jerk方程

应用优化的同伦分析法计算了具有三次非线性项的三阶微分方程(Jerk)的近似周期和近似解析周期解。给出一个算例说明由优化的同伦分析法可以容易得到精确的二阶近似周期解。当初速度a比较大时,一阶近似周期与精确周期的百分比误差为-0.415%,而二阶近似周期与精确周期的百分比误差为-0.0298%。与数值方法给出的"精确"周期解比较,一阶近似解析周期解和二阶近似周期解的精度很高。这个说明同伦分析法对求解非线性Jerk方程非常有效。

一种基于Jerk模型的机动目标单站无源定位算法

针对采用非线性较强的观测角、角度变化率、脉冲到达时间差等参数的单站无源定位跟踪系统,提出了一种新的跟踪滤波算法IMM-Jerk。该方法用Jerk模型对做复杂机动的运动目标建模,采用经过UKF滤波改进的交互多模(IMM)算法对目标实现跟踪滤波。该算法可适用于对做多种机动运动的目标的跟踪,提高了目标跟踪收敛精度和跟踪系统的稳定性。仿真试验证明了该方法的可行性和有效性,并具有较高的应用价值。最后,对IMM-Jerk算法的研究方向进行了讨论。