Low-Dimensional Dynamical Systems for a Wake-Type Shear Flow with Vortex Dislocations

Low-dimensional systems are constructed to investigate dynamics of vortex dislocations in a wake-type shear flow. High-resolution direct numerical simulations are employed to obtain flow snapshots from which the most energetic modes are extracted using proper orthogonal decomposition (POD). The first 10 modes are classified into two groups. One represents the general characteristics of two-dimensional wake-type shear flow, and the other is related to the three-dimensional properties or non-uniform characteristics along the span. Vortex dislocations are generated by these two kinds of coherent structures. The results from the first 20 three-dimensional POD modes show that the low- dimensional systems have captured the basic properties of the wake-type shear flow with vortex dislocation, such as two incommensurable frequencies and their beat frequency.

Heteroclinic cycles in lattice dynamical systems

A criterion of spatial chaos occurring in lattice dynamical systems-heteroclinic cycle-is discussed. It is proved that if the system has asymptotically stable heteroclinic cycle, then it has asymptotically stable homoclinic point which implies spatial chaos.

Suppressing chaos and transient in parameter perturbed systems

The systems with some system parameters perturbed are investigated. These systems might exist in nature or be obtained by perturbation or truncation theory. Chaos might be suppressed or induced. Some of these dynamical systems exhibit extraordinary long transients, which makes the temporal structure seem sensitively dependent on initial conditions in finite observation time interval.

A new method of studying the dynamical behavior of the sine-gordon equation

We try to connect the theory of infinite dimensional dynamical systems and nonlinear dynamical methods. The sine-Gordon equation is used to illustrate our method of discussing the dynamical behaviour of infinite dimensional systems. The results agree with those of Bishop and Flesch [SLAM J. Math. Anal. 21 (1990) 1511].

On properties of hyperchaos: Case study

Some properties of hyperchaos are exploited by studying both uncoupled and coupled CML. In addition to usual properties of chaotic strange attractors, there are other interesting properties, such as: the number of unstable periodic points embedded in the strange attractor increases dramatically increasing and a large number of low-dimensional chaotic invariant sets are contained in the strange attractor. These properties may be useful for regarding the edge of chaos as. the origin of complexity of dynamical systems.

Predicting chaotic time-series with wavelet networks

A new technique, wavelet network, is introduced to predict chaotic time series. By using this technique, firstly, we make accurate short-term predictions of the time series from chaotic attractors. Secondly, we make accurate predictions of the values and bifurcation structures of the time series from dynamical systems whose parameter values are changing with time. Finally we predict chaotic attractors by making long-term predictions based on remarkably few data points, where the correlation dimensions of predicted attractors are calculated and are found to be almost identical to those of actual attractors.

An adaptive controller for a class of nonlinear system using direction basis function

For a class of nonlinear dynamical systems, the adaptive controllers are investigated using direction basis function (DBF) in this paper. Based on the criterion of Lyapunov' stability, DBF is designed which guarantees that the output of the controlled system asymptotically tracks the reference signals. Finally, the simulation shows the good tracking effectiveness of the adaptive controller.

基于复合离散混沌动力系统的序列密码算法

利用复合离散混沌系统的特性,提出了两个基于复合离散混沌系统的序列密码算法.算法的加密和解密过程都是同一个复合离散混沌系统的迭代过程,取迭代的初始状态作为密钥,以明文序列作为复合系统的复合序列,它决定了迭代过程中迭代函数的选择(或明文与密钥),然后将迭代轨迹粗粒化后作为密文.由于迭代对初始条件的敏感性和迭代函数选择的随机性,密钥、明文与密文之间形成了复杂而敏感的非线性关系,而且密文和明文的相关度也很小,从而可以有效地防止密文对密钥和明文信息的泄露.复合离散混沌系统均匀的不变分布还使密文具有很好的随机特性.经分析表明,系统具有很高的安全性.

陡坡带砂砾岩体油气成藏模式研究——以东营凹陷西北部陡坡带为例

Based on the study of sequence stratigraphy, modern sedimentary, basin analysis, and petroleum system in abrupt slop of depression, this paper builds sedimentary system and model, sandy bodies distribution, and pool-forming mechanism of subtle trap. There are some conclusions and views as follows. By a lot of well logging and seismic analysis, the author founded up the sequence stratigraphic of the abrupt slope, systematically illustrated the abrupt slope constructive framework, and pointed out that there was a special characteristics which was that south-north could be divided to several fault block and east-west could be carved up groove and the bridge in studying area. Based all these, the author divided the studying area to 3 fault block zone in which because of the groove became the basement rock channel down which ancient rivers breathed into the lake, the alluvial fan or fan delta were formed. In the paper, the author illustrated the depositional system and depositional model of abrupt slope zone, and distinguished 16 kinds of lithofacies and 3 kinds of depositional systems which were the alluvial fan and fan-delta system, lake system and the turbidite fan or turbidity current deposition. It is first time to expound completely the genetic pattern and distributing rule of the abrupt slope sandy-conglomeratic fan bodies. The abrupt slope sandy-conglomeratic fan bodies distribute around the heaves showing itself circularity shape. In studying area, the sandy-conglomeratic fan bodies mainly distribute up the southern slope of Binxian heave and Chenjiazhuang heave. There mainly are these sandy-conglomeratic fan body colony which distributes at a wide rage including the alluvial fan, sub-water fluvial and the turbidite fan or the other turbidity current deposition in the I fault block of the Wangzhuang area. In the II fault block there are fan-delta front and sub-water fluvial. And in the Binnan area, there mainly are those the alluvial fan (down the basement rock channel) and the sandy-conglomeratic fan body which formed as narrowband sub-water fluvial (the position of bridge of a nose) in the I fault block, the fan-delta front sandy-conglomeratic fan body in the H fault block and the fan-delta front and the turbidity current deposition sandy-conglomeratic fan body in the m fault block. Based on the reservoir outstanding characteristics of complex classic composition and the low texture maturity, the author comparted the reservoir micro-structure of the Sha-III and Sha-IV member to 4 types including the viscous crude cementation type, the pad cementation type, the calcite pore-funds type and the complex filling type, and hereby synthetically evaluated 4 types sandy- conglomeratic fan body reservoir. In the west-north abrupt slope zone of Dongying Depression, the crude oil source is belonging to the Sha-III and Sha-IV member, the deep oil of Lijin oilfield respectively come from the Sha-III and Sha-IV member, which belongs to the autogeny and original deposition type; and the more crude oil producing by Sha-IV member was migrated to the Wangzhuan area and Zhengjia area. The crude oil of Binnan oil-field and Shanjiasi oil-field belongs to mixed genetic. It is the first time to illustrate systematically the genetic of the viscous crude that largely being in the studying area, which are that the dissipation of the light component after pool-forming, the biological gradation action and the bath-oxidation action, these oil accumulation belonging to the secondary viscous crude accumulation. It is also the first time to compart the studying area to 5 pool-forming dynamical system that have the characteristic including the common pressure and abnormal pressure system, the self-fountain and other-fountain system and the closing and half-closing system etc. The 5 dynamical systems reciprocally interconnected via the disappearance or merger of the Ethology and the fluid pressure compartment zone, the fault and the unconformity surface, hereby formed duplicated pattern oil-gas collecting zone. Three oil-gas pool-forming pattern were founded, which included the self-fountain side-direction migrated collecting pattern, the self-fountain side-direction ladder-shape pool-forming pattern and the other-fountain pressure releasing zone migrated collecting pattern. A series of systemic sandy-conglomeratic fan bodies oil-gas predicting theory and method was founded, based on the groove-fan corresponding relation to confirm the favorable aim area, according as the characteristic of seismic-facies to identify qualitatively the sandy-conglomeratic fan bodies or its scale, used the temporal and frequency analysis technique to score the interior structure of the sandy- conglomeratic fan bodies, applied for coherent-data system analysis technology to describe the boundary of the sandy-conglomeratic fan bodies, and utilized the well logging restriction inversion technique to trace quantificational and forecast the sandy-conglomeratic fan bodies. Applied this technique, totally 15 beneficial sandy-conglomeratic fan bodies were predicted, in studying area the exploration was preferably guided, and the larger economic benefit and social benefit was acquired.

Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

Multiscale Coupling in Complex Mechanical Systems

Multiscale coupling attracts broad interests from mechanics, physics and chemistry to biology. The diversity and coupling of physics at different scales are two essential features of multiscale problems in far-from-equilibrium systems. The two features present fundamental difficulties and are great challenges to multiscale modeling and simulation. The theory of dynamical system and statistical mechanics provide fundamental tools for the multiscale coupling problems. The paper presents some closed multiscale formulations, e.g., the mapping closure approximation, multiscale large-eddy simulation and statistical mesoscopic damage mechanics, for two typical multiscale coupling problems in mechanics, that is, turbulence in fluids and failure in solids. It is pointed that developing a tractable, closed nonequilibrium statistical theory may be an effective approach to deal with the multiscale coupling problems. Some common characteristics of the statistical theory are discussed.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time-series

We propose here a local exponential divergence plot which is capable of providing an alternative means of characterizing a complex time series. The suggested plot defines a time-dependent exponent and a ''plus'' exponent. Based on their changes with the embedding dimension and delay time, a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time, and the largest Lyapunov exponent has been obtained. When redefining the time-dependent exponent LAMBDA(k) curves on a series of shells, we have found that whether a linear envelope to the LAMBDA(k) curves exists can serve as a direct dynamical method of distinguishing chaos from noise.

The strange attractor of a kind of 2-dimensional map and dynamical properties on it

On the basis of previous works, the strange attractor in real physical systems is discussed. Louwerier attractor is used as an example to illustrate the geometric structure and dynamical properties of strange attractor. Then the strange attractor of a kind of two-dimensional map is analysed. Based on some conditions, it is proved that the closure of the unstable manifolds of hyberbolic fixed point of map is a strange attractor in real physical systems.