A stream cipher based on a spatiotemporal chaotic system

A stream cipher based on a spatiotemporal chaotic system is proposed. A one-way coupled map lattice consisting of logistic maps is served as the spatiotemporal chaotic system. Multiple keystreams are generated from the coupled map lattice by using simple algebraic computations, and then are used to encrypt plaintext via bitwise XOR. These make the cipher rather simple and efficient. Numerical investigation shows that the cryptographic properties of the generated keystream are satisfactory. The cipher seems to have higher security, higher efficiency and lower computation expense than the stream cipher based on a spatiotemporal chaotic system proposed recently.     

Computation of focus values with applications

Computation of focus (or focal) values for nonlinear dynamical systems is not only important in theoretical study, but also useful in applications. In this paper, we compare three typical methods for computing focus values, and give a comparison among these methods. Then, we apply these methods to study two practical problems and Hilbert's 16th problem. We show that these different methods have the same computational complexity. Finally, we discuss the “minimal singular point value” problem.     

A two-step phase-retrieval method in Fourier-transform ghost imaging

A two-step phase-retrieval method, based on Fourier-transform ghost imaging, was demonstrated. For the complex objects, the phase-retrieval process was divided into two steps: first got the complex object’s amplitude from the Fourier-transform patterns of the squared object function, then combining with the Fourier-transform patterns of the object function to get the phase. The theoretical basis of this technique is outlined, and the experimental results are presented.     

强度关联三维衍射层析的实验研究

提出了一种基于强度关联成像的新型三维衍射层析技术.利用强度关联成像技术(鬼成像)可实现无透镜傅里叶变换的特点,并结合衍射层析技术和二步相位恢复算法,使用波长为650 nm的赝热光实现了强度关联三维衍射层析.详细描述了强度关联三维衍射层析的基本原理以及具体实验结果,为在第三代同步辐射光源实现非相干X光衍射成像积累了经验.     

Generating chaos with a switching piecewise-linear controller

This paper introduces a new chaos generator, a switching piecewise-linear controller, which can create chaos from a three-dimensional linear system within a wide range of parameter values. Basic dynamical behaviors of the chaotic controlled system are investigated in some detail. (c) 2002 American Institute of Physics.     

Anticontrol of chaos in continuous-time systems via time-delay feedback

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.     

一个稳态PDE系统的状态约束极小能最优控制问题

本文研究一个由偏微分方程描述的调和型稳态系统带不等式或光顺约束条件的极小能最优控制问题。基于由笔者新近发展的样条函数最优解技术,我们对所论问题可以给出完整的显式解析型最优解。问题的最优解可以通过一种优雅的再生核结构来表达。这种新技巧还可以用来对其他不同领域如图象和信号的最优再现等问题作统一的处理,体现出样条函数新理论的优越性。 这种样条函数技巧的前身只能解决由常微分方程描述的集中参数系统问题。有关这方面的历史发展和评述可参阅笔者下面的综合报告。本文的结果是这一研究方向的新发展。     

Chaotic Vibrations of the One-Dimensional Wave Equation Due to a Self-Excitation Boundary Condition Part I: Controlled hysteresis

The study of nonlinear vibrations/oscillations in mechanical and electronic systems has always been an important research area. While important progress in the development of mathematical chaos theory has been made for finite dimensional second order nonlinear ODEs arising from nonlinear springs and electronic circuits, the state of understanding of chaotic vibrations for analogous infinite dimensional systems is still very incomplete.

The 1-dimensional vibrating string satisfying on the unit interval is an infinite dimensional harmonic oscillator. Consider the boundary conditions: at the left end , the string is fixed, while at the right end , a nonlinear boundary condition , takes effect. This nonlinear boundary condition behaves like a van der Pol oscillator, causing the total energy to rise and fall within certain bounds regularly or irregularly. We formulate the problem into an equivalent first order hyperbolic system, and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary condition. Since the solution of the first order hyperbolic system depends completely on this nonlinear relation and its iterates, the problem is reduced to a discrete iteration problem of the type , where is the nonlinear reflection relation. We say that the PDE system is chaotic if the mapping is chaotic as an interval map. Algebraic, asymptotic and numerical techniques are developed to tackle the cubic nonlinearities. We then define a rotation number, following J.P. Keener , and obtain denseness of orbits and periodic points by either directly constructing a shift sequence or by applying results of M.I. Malkin to determine the chaotic regime of for the nonlinear reflection relation , thereby rigorously proving chaos. Nonchaotic cases for other values of are also classified. Such cases correspond to limit cycles in nonlinear second order ODEs. Numerical simulations of chaotic and nonchaotic vibrations are illustrated by computer graphics.

     

Stability of piecewise affine systems with application to chaos stabilization

This paper addresses the stability issue for a class of piecewise affine (PWA) systems, where the state spaces are assumed to be dividable into a certain number of hypercuboid subspaces. By constructing appropriate piecewise continuous Lyapunov functions, several numerically tractable stability criteria are developed for four subclasses of such PWA systems, which allow to recast the switching control problem for the PWA systems as a convex optimization problem. Moreover, the proposed method is applied to switching controller design for (globally and locally) stabilizing the unstable equilibrium points of PWA chaotic systems. Numerical simulations on the chaotic Chua's circuit are presented to verify the theoretical results.     

Lower-order state-space self-tuning control for a stochastic chaotic hybrid system

^** Email: shtsai{at}mail.ncku.edu.tw In this paper, subject to acceptable closed-loop performance,an effective lower-order tuner for a stochastic chaotic hybridsystem is designed using the observer/Kalman filter identification(OKID) method, in which the system state in a general coordinateform is transformed to one in an observer form. The OKID methodis a time-domain technique that identifies a discrete input–outputmap by using known input–output sampled data in the generalcoordinate form, through an extension of the eigensystem realizationalgorithm. Moreover, it provides a lower-order realization ofthe tracker, with computationally effective initialization,for on-line "auto-regressive moving average process with exogenousmodel" -based identification and a lower-order state-space self-tuningcontrol technique. Finally, the chaotic Chen's system is usedas an illustrative example to demonstrate the effectivenessof the proposed methodology.