低Reynold数圆柱尾流中混沌运动研究

本文以混沌的观点研究流体湍流.在Reynold数为63—179的范围内,在低湍流度水洞中,在圆柱体尾流中测量速度脉动,获得关联维数、相空间轨迹、谱分布等有用数据,并做了流场显示.实验结果表明,该种开放型流动的早期转捩过程中,存在混沌现象.这有助于进一步认识开放型流动中湍流发生的机制.     

旋转流动的低模分析及仿真研究

为了探讨Couette-Taylor流从层流到湍流过渡的方式以及流动发展到湍流之后混沌吸引子的某些特征等问题,采用低模分析方法研究了Couette-Taylor流的部分动力学行为及仿真问题,讨论了Couette-Taylor流三模态类Lorenz型方程组的动力学行为,包括定态的失稳、极限环的出现、分岔与混沌的演变和全局稳定性分析等。通过线性稳定性分析和数值模拟等方法给出了此三维模型分岔与混沌等动力学行为及其演化历程,并借此解释了Couette-Taylor流试验中观察到的部分涡流的演化过程.基于系统的分岔图、Lyapunov指数谱、功率谱、Poincaré(庞加莱)截面和返回映射等揭示了系统混沌行为的普适特征.     

旋转流动混沌行为的全局稳定性分析及数值仿真

同轴圆筒间旋转流动的Couette-Taylor流问题是近一个世纪以来人们普遍关注的热点问题,由于其流动形态的可观测性以及它在湍流研究中的基础性地位及其在流体机械、石油化工等领域的广泛应用,国际上将其列为非线性科学的范例之一.为了探讨这种流动从层流到湍流过渡的方式以及流动发展到湍流之后混沌吸引子的某些特征等问题,该文采用低模分析方法研究了Couette-Taylor流的部分动力学行为及仿真问题,探讨了同轴圆筒间Couette-Taylor流三模态类Lorenz型方程组的动力学行为及仿真问题,数值模拟了系统分岔与混沌的演变历程,讨论了系统的全局稳定性.     

宾汉流体稠密两相湍流流动中的二阶矩模型

建立的Bingham流体稠密两相流动的二阶矩-颗粒动力论湍流模型（USM-theta模型）既体现了两相的作用,又体现了屈服应力所引起的附加项,并提出了USM-theta模型下考虑浓度修正值影响的两相湍流流动的算法．利用该模型对圆管内Bingham流体的单相湍流流动、稠密液固两相的湍流流动进行了计算,并和五方程湍流模型进行了比较,结果表明该模型的预测效果更好．利用USM-theta模型对含颗粒的Bingham流体的两相湍流流动进行了模拟,随着屈服应力的增加,Bingham流体相与颗粒相在管道中心附近的主流速度减小．液固两相湍流和Bingham流体两相湍流的计算结果表明屈服应力引起的附加项对流动有很重要的影响．     

二维耦合Logistic映射的动力学性质及在流密码生成中的应用

本文研究了带二次耦合项的二维Logistic映射的性质和分岔行为,数值模拟了混沌的生成过程．若控制一个参数值近似为1,则产生近乎满的混沌区．这种混沌区产生的随机序列所生成的流密码具有很好的0-1分布、高线性复杂性、密钥敏感性等．最后给出了用于保密通信的模型．     

旋流式系统类Lorenz方程组的动力学行为及仿真

正1引言国内外众多学者对同轴圆柱间旋转流动Couette-Taylor流问题的复杂动力学行为进行了大量深入的研究,相关文献非常丰富~([1-11]).这种流动存在着多种演化到湍流的方式,提供了从层流到湍流过渡非常好的例子.目前的研究主要是利用分歧理论来解释和分析实验中观察到的流动发展到湍流前的各种涡流及其相互演化的过程,以及从层流过渡到湍流的方式及仿真等,而对流动发展到湍流之后混沌吸引子的存在性及仿真等问题目前很少有文献涉及.由以往的实验研究可知,随雷诺数的增大,这种流动最终总要演化成湍     

单向耦合双稳映象格子从时空准周期过渡到混沌

研究了描述开流系统的单向耦合双稳映象格子模型 (OCBL) .通过数值模拟发现了时空准周期现象 .给出了时空准周期等主要动力学行为在参量平面上的相图并讨论了从时空准周期到混沌的转化过程 .结果对了解湍流的发生机制可能具有重要意义 .     

两个模态耦合的Ginzburg-Landau方程的时空混沌同步化

根据数值计算的结果提出了模态耦合的条件,两个方程在高频模态上是耦合的,而在低频模态上是不耦合的．利用了无穷维动力系统理论,证明了两个高频模态耦合的Ginzburg-Landau方程在函数空间中存在吸引域,因而存在连通的、有限维的紧的整体吸引子．驱动方程存在时空混沌．将方程组联系一个截断形式,得到的修正方程组将保持原方程组的动力学行为．高频模态耦合的两个方程在一定的条件下具有挤压性质,证明了可达到完全的时空混沌同步化．在数学上定性解释了无穷维动力系统的同步化现象．研究方法不同于有限维动力系统中通常使用的Liapunov函数方法与近似线性方法．     

浅水方程近岸行为的数值模拟

二维浅水流动几乎仅在水平方向上,这一特点容许在数学形式上对ＮＳ方程进行简化：通过描述水流运动的平均行为而使得问题降低一维［１０］,从而在数值上表现为大大减少计算量,这一相对简单性正是浅水方程之所以吸引如此多的计算数学家和流体力学家关注的原因之一．通过降维而减少计算量的思想在深水方程中表现为通过边界积分法而捕捉气液交界面的行为［１］． 浅水方程的数值模拟在计算机出现的早期就开始得到应用．在本世纪四十年代后期,Ｃｈａｒｎｅｙ等人就利用它做了大气的数值模拟［２］,Ｈａｎｓｅｎ数值模拟了海洋流动［５］．…     

粉末注射成形填充过程的数值模拟

本文将粉末注射成形喂料在薄壁模腔中的流动视为二维流动，以流变学的基本方程为基础，建立了从动量方程、连续方程和热传递方程得到的描述PIM喂料充模二维流动的数学模型。在无滑移边界的条件下，推导了喂料熔体流导率的计算公式和压力场的控制方程，得到的压力场控制方程是一非线性椭圆偏微分方程．从而可用Galerkin方法进行数值求解，使模型的数值求解成为可能，为进一步对粉末注射成形进行计算机模拟和数值分析奠定了数学基础。     

A new auto-switched chaotic system and its FPGA implementation

This paper presents a 3D chaotic system which is constructed by an auto-switched numerical resolution of multiple three dimensional continuous chaotic systems. The designed chaotic system provides complex chaotic attractors and can change its behaviors automatically via a chaotic switching-rule. Some complex dynamical behaviors are investigated and analyzed. The originality of the proposed architecture is that allows to solve the problem of the finite precision due to the digital implementation while provides a good trade-off between high security, performance and hardware resources (low power and cost). Hardware digital implementation and FPGA circuit experimental results demonstrate a promising technique can be applied in efficient embedded ciphering communication systems. Moreover, the proposed chaotic system should be very useful for the consideration of reducing negative influence of dynamical degradation in real-time embedded applications.     

A new butterfly-shaped attractor of Lorenz-like system

In this letter a new butterfly-shaped chaotic attractor is reported. Some basic dynamical properties, such as Poincare mapping, Lyapunov exponents, fractal dimension, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied. Furthermore, we clarify that the chaotic attractors of the system is a compound structure obtained by merging together two simple attractors through a mirror operation.     

无力磁场和Beltrami流

场矢量处处平行其旋度的管式矢量场具有复杂的拓扑结构．而且通常表现出混饨行为．本文提供了具有常数比例因子的这类矢量场在三种基本坐标系内的解析解,并指出完全导电流体内的一个Beltrami流能维持一个定常无力磁场,如果磁场矢量处处平行速度．     

Mathematical Models of the Twin-T,Wien-bridgeand Family of Minimum Component Electronic ChaosGenerators with Demonstrative Recurrence Plots

Mathematical models describing the chaotic behaviours in the recently reportedTwin-T, Wien-bridge and family of minimum component electronic chaos generators are derived.Nonideal effects of the active element in these circuits are integrated into analysis where necessarywhile a two segment piece-wise-linear approximation of the passive nonlinear voltage controlledresistor characteristics is adopted. The chaotic behaviour is shown to extend to the case where anactive nonlinear resistor with odd symmetrical characteristics is used. Three dimensional chaoticattractors obtained from numerical integrations of the proposed mathematical models areconstructed. Demonstrative recurrence plots are included.     

Generation of complex phenomena in a simple electromechanical system using the feedback control

In this Letter, a feedback control method is proposed for generation of some interesting complex behaviors in electromechanical devices. The controllers for linear electromechanical systems based on the Power Supply Feedback Control are designed and their mathematical models are obtained. Computer simulations of the controlled systems show complex dynamical behaviors such as jump phenomenon, Sommerfeld effect, period-nT and chaotic oscillations.     

Analysis and circuitry realization of a novel three-dimensional chaotic system

In this paper a new three-dimensional chaotic system is introduced. Some basic dynamical properties are analyzed to show chaotic behavior of the presented system. These properties are covered by dissipation of system, instability of equilibria, strange attractor, Lyapunov exponents, fractal dimension and sensitivity to initial conditions. Through altering one of the system parameters, various dynamical behaviors are observed which included chaos, periodic and convergence to an equilibrium point. Eventually, an analog circuit is designed and implemented experimentally to realize the chaotic system.     

Bifurcations and chaos of a discrete mathematical model for respiratory process in bacterial culture

The discrete mathematical model for the respiratory process in bacterial culture obtained by Euler method is investigated. The conditions of existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, condition of existence of chaos in the sense of Marotto＇s definition of chaos is proved. The bifurcation diagrams, Lyapunov exponents and phase portraits are given for different parameters of the model, and the fractal dimension of chaotic attractor was also calculated. The numerical simulation results confirm the theoretical analysis and also display the new and complex dynamical behaviors compared with the continuous model. In particular~ we found that the new chaotic attractor, and new types of two or four coexisting chaotic attractors, and two coexisting invariant torus.     

A hyperchaotic system from a chaotic system with one saddle and two stable node-foci

This paper presents a 4D new hyperchaotic system which is constructed by a linear controller to a 3D new chaotic system with one saddle and two stable node-foci. Some complex dynamical behaviors such as ultimate boundedness, chaos and hyperchaos of the simple 4D autonomous system are investigated and analyzed. The corresponding bounded hyperchaotic and chaotic attractor is first numerically verified through investigating phase trajectories, Lyapunove exponents, bifurcation path, analysis of power spectrum and Poincaré projections. Finally, two complete mathematical characterizations for 4D Hopf bifurcation are rigorous derived and studied.     

STUDY ON A THREE DIMENSIONAL CHAOTIC SYSTEM

In this letter a new chaotic system is discussed. Some basic dynamic properties, such as symmetry, dissipation, continuous spectrum and chaotic behaviors of the butterfly attractor are studied. Furthermore, period-doubling bifurcations in a system with definite parameters has been investigated.