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1.
Ma Jun-hai Associate Professor Doctor Chen Yu-shu Professor Doctor Director 《应用数学和力学(英文版)》2000,21(11):1237-1245
The state space reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: N.H.Packard, F.Takens, M. Casdagli, J.F.Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time τ were identified. The influence for state space reconstruction of lag time τ was discussed. The result tells us that is a good practical method for state space reconstruction. 相似文献
2.
The state space reconstruction technology of different kinds of chaotic data obtained from dynamical system 总被引:7,自引:0,他引:7
Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the
practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the
ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical
data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate
the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the
basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors
of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different
kinds of chaotic data obtained from dynamical system has also been discussed in detail.
The project supported by the National Natural Science Foundation of China (19672043) 相似文献
3.
NECESSARYANDSUFFICIENTCRITERIAFORABSOLUTESTABILITYOFTHEDIRECTCONTROLSYSTEMZhangJi-ye(张继业);ShuZhong-zhou(舒仲周)(DepartmentofEngi... 相似文献
4.
In this topic, a new approach to the analysis of time-variation dynamics is proposed by use of Legendre series expansion and
Legendre integral operator matrix. The theoretical basis for effective solution of time-variation dynamics is therefore established,
which is beneficial to further research of time-variation science.
Supported by Shanghai Key Project Research Foundation. 相似文献
5.
In this paper several explicit criterions of absolute stability for the real second canonical form of control system are giyen, which generalize and include the known result in ref [2]. By appiyung then criterions to the well known equations of the longitudinal motion of aireraft aresult that generalizes and includes the known results in refs. [3,4,2] is obtained. 相似文献
6.
IntroductionConsidertheindirectcontrolsystem x =Ax Bφ(σ) , σ =CTx ρφ(σ) ,(1 )wherex∈Rn,σ ∈R ,Aisn×nstablematrix ,BandCarendimensionalvectors,thesymbolTstandsfortransposition ,ρisaconstant,function φ(σ) :R →Riscontinuousandsatisfiesconditionσφ(σ) >0 ( σ∈R ,σ≠ 0 ) . (2 )Manyspe… 相似文献
7.
高国成 《应用数学和力学(英文版)》1993,14(5):469-479
In this paper,some explicit criteria of absolute stability for the trivial solution of the real second canonical form of nonlinear control system are given,which include and improve the criteria in paper[1].By applying these criteria to the well-known equation of the longitudinal motion of aircraft,some results are obtained,which include and improve the corresponding results in papers[1,2,3,4]. 相似文献
8.
Necessary and sufficient conditions for the absolute stability of discrete type lurie control system 总被引:1,自引:0,他引:1
张继业 《应用数学和力学(英文版)》1995,16(10):995-1001
NECESSARYANDSUFFICIENTCONDITIONSFORTHEABSOLUTESTABILITYOFDISCRETETYPELURIECONTROLSYSTEMZhangJiye(张继业)(ReceixedOct.5.1994Commu... 相似文献
9.
This work investigates the trajectory method [1] for thereconstruction of ordinary differential equations (ODEs) from timeseries. The potentials of the method are analyzed for dynamical systemsdescribed by second- and third-order ODEs, focusing in particular on therole of the parameters of the method and on the influence of the qualityof the time series in terms of noise, length and sampling frequency.Typical models are investigated, such as the van der Pol, the linearmechanical, the Duffing and the Rössler equations, resulting in arobust and versatile method which is capable of allowing interestingapplications to experimental cases. The method is then applied to themeasured time series of a nonlinear mechanical oscillator, a typicalvelocity oscillation of the bursting phenomenon in near-wall turbulenceand the averaged annual evolution of rainfall, temperature andstreamflow over a hydrological basin. 相似文献
10.
为了适应低成本快速响应卫星的发展趋势,越来越多的卫星采用了MEMS陀螺系统与信息融合方法相结合的设计方案。为提高传统的基于自回归滑动平均(Auto-Regressive and Moving Average,ARMA)模型和支持度的信息融合方法的精度,抑制随机误差趋势项对卫星稳定控制的不利影响,提出了一种基于支持向量回归机(Support Vector Regression,SVR)的预测补偿算法。该算法对各个MEMS陀螺输出数据进行滤波,并提取相应的随机误差趋势项,通过相空间重构获得训练样本并进行SVR建模,用以实时补偿。然后使用低成本商用器件搭建了MEMS陀螺系统,并在单轴气浮转台上进行了实验。实验结果表明,预测补偿算法使得MEMS陀螺系统输出数据的方差降为原先的31.39%,融合精度得到了显著的提高。 相似文献
11.
12.
ONTHESTABILITYOFFORCEDDISSIPATIVENONLINEARSYSTEM¥ChenDaduan(陈达段)LiuXiaoming(刘晓明)ShiWeihui(施惟慧)(ShanghaiUniversity.Shanghai200... 相似文献
13.
赵俊三 《应用数学和力学(英文版)》1988,9(11):1097-1100
As to an autonomous nonlinear system, the stability of the equilibrium state in a sufficiently small neighborhood of the equilibrium
state can be determined by eigenvalues of the linear part of the nonlinear system provided that the eigenvalues are not in
a critical case. Many methods may be used to detect the stability for a linear system. A lot of researches for determining
the stability of a nonlinear system are completed by mathematicians and mechanicians but most of them are methods for the
special forms of nonlinear systems. Till now, none of these methods can be conveniently applied to all nonlinear systems.
The method introduced by this paper gives the necessary and sufficient conditions of the stability of a nonlinear system.
The familiar Krasovski's method is a special case of this method. 相似文献
14.
M. M. Ramazanov 《Fluid Dynamics》2014,49(5):585-595
The conditions under which natural convection is absent from compressible fluids are investigated. It is shown that in the parameter “Rayleigh number-given temperature difference” plane there is a domain in which convection occurs for neither Rayleigh numbers. It is proposed to refer to this domain as the absolute convective stability region and to name the criterion determining the boundary of this region the absolute convective stability criterion. The necessary, sufficient, and necessary and sufficient conditions of the absolute convective stability for a viscous compressible fluid are derived. It is shown that in the particular case in which the thermal properties of the fluid and the adiabatic gradient are constant, these conditions coincide with the Schwarzschild criterion. 相似文献
15.
16.
Study on the Prediction Method of Low-Dimension Time Series that Arise from the Intrinsic Nonlinear Dynamics 总被引:1,自引:0,他引:1
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 相似文献
17.
张维 《应用数学和力学(英文版)》1989,10(10):955-967
In this paper, we give necessary and sufficient conditions for absolute stability of several classes of direct control systems, and discuss the absolute stability of the first canonical form of control system. The corresponding results in references [3,5,6] and [7] are improved.This paper is completed under the direct guidance and encouragement of professor Liao Xiaoxin and professor Deng Zhong-qi. The writer especially acknowledges their help. 相似文献
18.
This paper addresses the problem of resampling chaotic time series. We propose a method based on resampling distances between nearest neighbours in phase space, so that the resampled time series present the original points differently positioned along the trajectory. This approach allows one to obtain time series with the same length of the original one, so that confidence intervals for Lyapunov exponents, correlation dimension and other invariants would be determined. For its generality this kind of resampling would be applicable to chaotic time series no matter the observations concern natural or life sciences. The method has been tested with common simulated chaotic systems with both clean and noisy data. Short and noisy time series, as the ones we simulated, typically occur in medicine, biology, and social sciences. 相似文献
19.
M.P. Lazarevi 《Mechanics Research Communications》2006,33(2):269-279
A finite time stability test procedure is proposed for robotic system where it appears a time delay in PDα fractional control system. Paper extends some basic results from the area of finite time and practical stability to linear, continuous, fractional order time invariant time-delay systems given in state-space form. Sufficient conditions for this kind of stability, for particular class of fractional time-delay systems are derived. 相似文献