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.

Non-commutative symbolic coding

Gohm, Rolf; Kummerer, B.; Lang, T., (2006) 'Non-commutative symbolic coding', Ergodic Theory and Dynamical Systems 26(5) pp.1521-1548 RAE2008

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Broadband chaos generated by an optoelectronic oscillator.

We study an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive approximate mappings that do an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks.

Invariant measure selection by noise. An example

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on the specifics of the stochastic forcing.

Sensitivity to switching rates in stochastically switched ODEs

We consider a stochastic process driven by a linear ordinary differential equation whose right-hand side switches at exponential times between a collection of different matrices. We construct planar examples that switch between two matrices where the individual matrices and the average of the two matrices are all Hurwitz (all eigenvalues have strictly negative real part), but nonetheless the process goes to infinity at large time for certain values of the switching rate. We further construct examples in higher dimensions where again the two individual matrices and their averages are all Hurwitz, but the process has arbitrarily many transitions between going to zero and going to infinity at large time as the switching rate varies. In order to construct these examples, we first prove in general that if each of the individual matrices is Hurwitz, then the process goes to zero at large time for sufficiently slow switching rate and if the average matrix is Hurwitz, then the process goes to zero at large time for sufficiently fast switching rate. We also give simple conditions that ensure the process goes to zero at large time for all switching rates. © 2014 International Press.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Learning soft computing control strategies in a modular neural network architecture

Modelling and control of nonlinear dynamical systems is a challenging problem since the dynamics of such systems change over their parameter space. Conventional methodologies for designing nonlinear control laws, such as gain scheduling, are effective because the designer partitions the overall complex control into a number of simpler sub-tasks. This paper describes a new genetic algorithm based method for the design of a modular neural network (MNN) control architecture that learns such partitions of an overall complex control task. Here a chromosome represents both the structure and parameters of an individual neural network in the MNN controller and a hierarchical fuzzy approach is used to select the chromosomes required to accomplish a given control task. This new strategy is applied to the end-point tracking of a single-link flexible manipulator modelled from experimental data. Results show that the MNN controller is simple to design and produces superior performance compared to a single neural network (SNN) controller which is theoretically capable of achieving the desired trajectory. (C) 2003 Elsevier Ltd. All rights reserved.

Direct, positive feedbacks produce instability in models of interrelationships among soil structure, plants and arbuscular mycorrhizal fungi

Current conceptual models of reciprocal interactions linking soil structure, plants and arbuscular mycorrhizal fungi emphasise positive feedbacks among the components of the system. However, dynamical systems with high dimensionality and several positive feedbacks (i.e. mutualism) are prone to instability. Further, organisms such as arbuscular mycorrhizal fungi (AMF) are obligate biotrophs of plants and are considered major biological agents in soil aggregate stabilization. With these considerations in mind, we developed dynamical models of soil ecosystems that reflect the main features of current conceptual models and empirical data, especially positive feedbacks and linear interactions among plants, AMF and the component of soil structure dependent on aggregates. We found that systems become increasingly unstable the more positive effects with Type I functional response (i.e., the growth rate of a mutualist is modified by the density of its partner through linear proportionality) are added to the model, to the point that increasing the realism of models by adding linear effects produces the most unstable systems. The present theoretical analysis thus offers a framework for modelling and suggests new directions for experimental studies on the interrelationship between soil structure, plants and AMF. Non-linearity in functional responses, spatial and temporal heterogeneity, and indirect effects can be invoked on a theoretical basis and experimentally tested in laboratory and field experiments in order to account for and buffer the local instability of the simplest of current scenarios. This first model presented here may generate interest in more explicitly representing the role of biota in soil physical structure, a phenomenon that is typically viewed in a more process- and management-focused context. (C) 2011 Elsevier Ltd. All rights reserved.