Chaotic bursts in nonlinear dynamical systems

Several elementary nonlinear dynamical systems in the complex plane may provide models for abrupt transitions to chaotic dynamics. In particular, the complex trigonometric and exponential functions explode into chaos as a parameter is varied. Numerical evidence is presented that supports the contention that these explosions occur whenever an elementary bifurcation occurs. This numerical evidence, in the form of computer graphics, is an example of the increasing importance of experimentation in mathematics research.     

Resurrection of crushed magnetization and chaotic dynamics in solution NMR spectroscopy

We show experimentally and theoretically that two readily observed effects in solution nuclear magnetic resonance (NMR)-radiation damping and the dipolar field-combine to generate bizarre spin dynamics (including chaotic evolution) even with extraordinarily simple sequences. For example, seemingly insignificant residual magnetization after a crusher gradient triggers exponential regrowth of the magnetization, followed by aperiodic turbulent spin motion. The estimated Lyapunov exponent suggests the onset of spatial-temporal chaos and the existence of chaotic attractors. This effect leads to highly irreproducible experimental decays that amplify minor nonuniformities such as temperature gradients. Imaging applications and consequences for other NMR studies are discussed.     

神经网络对马尾松蛀干类害虫数量的混沌识别

[目的]检测马尾松蛀干类害虫2006～2010年,林间种群数量是否具有混沌特性。[方法]利用前馈神经网络分析马尾松蛀干类害虫林间种群数量的复杂性动态。[结果]前馈网络模型估计的最大Lyapunov指数为0.0128,说明马尾松蛀干类害虫林间种群序列存在混沌现象。[结论]马尾松蛀干类害虫的数量与前一次或前几次观测值密切相关,可用重构相空间的方法预测下一次观测值。     

带有反馈环节的装配系统的混沌特性研究

应用混沌学理论研究了带有正反馈环节的装配系统的特性,以缓冲区工件工件数量为状态变量,反馈作为控制变量,建立了装配系统的加工缓冲区的差分方程模型．通过Matlab仿真,绘制其分岔图及其Lyapunov指数谱,研究了装配系统的性能．结果表明,在正反馈环节的影响下,当反馈回来的次品数量占到它的加工工件的一定比例时,装配系统表现出混沌的特性,从而证明了装配系统的简单动力学方程蕴含着混沌．     

基于响应面方法的马尾松毛虫发生量混沌特性检测及其预测

以非线性动力学为基础,通过响应面方法建立马尾松毛虫有虫面积序列密度依赖离散世代的非线性模型.结果表明:用响应面方法检测的马尾松毛虫有虫面积序列具有混沌特征,马尾松毛虫世代间有虫面积动态为2级相关,可以用前1代及前2代的有虫面积预测下1代的有虫面积,且预测准确性较高.     

Waves of larch budmoth outbreaks in the European alps

Spatially extended population models predict complex spatiotemporal patterns, such as spiral waves and spatial chaos, as a result of the reaction-diffusion dynamics that arise from trophic interactions. However, examples of such patterns in ecological systems are scarce. We develop a quantitative technique to demonstrate the existence of waves in Central European larch budmoth (Zeiraphera diniana Gn.) outbreaks. We show that these waves travel toward the northeast-east at 210 kilometers per year. A theoretical model involving a moth-enemy interaction predicts directional waves, but only if dispersal is directionally biased or habitat productivity varies across the landscape. Our study confirms that nonlinear ecological interactions can lead to complex spatial dynamics at a regional scale.     

水平及倾斜管内间歇流向环状流转变的研究

对水平及倾斜管内油气两相间歇流向环状流的流型转变进行了实验和理论研究，根据实验中观察到的现象，提出了一个新的机理模型，并依据此机理模型合理地解释了环状流的形成。理论结果与实验数据吻合良好。     

Lattice effects observed in chaotic dynamics of experimental populations

Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated much ecological research; yet discrete-state models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discrete-state and continuous-state population models. Neither the discrete- nor continuous-state models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuous-state model and the cyclic dynamics predicted by the discrete-state models. We suggest that such lattice effects could be an important component of natural population fluctuations.     

Persistence of transients in spatially structured ecological models

Simple discrete-time ecological models for a species with alternating reproduction and dispersal are shown to have complex transient dynamics. If the density dependence (nonlinearity) is strong enough, then the time required to reach the final dynamics is usually very long, approaching thousands of generations, and there are typically very sudden changes in the form of the dynamics. Apparent chaos can change to cycles or vice versa. These results are consistent with observed sudden changes in the form of the dynamics of a single species and imply that transient dynamics of ecological models may be more relevant than long-term behavior.     

时滞反馈及轴力作用下弹性梁的非线性振动

基于时滞反馈控制策略及Euler-Bernoulli梁理论，建立了轴力作用下弹性支座压电耦合梁的非线性动力学模型.通过模态分析和线性稳定性分析，得到了压电耦合作用时滞反馈条件下的系统稳定性条件.采用Galerkin方法和非线性振动的多尺度法，从理论上推导出时滞动力系统的分岔响应.结果表明，对于某一确定的时滞，控制增益的变化可能会导致周期运动、拟周期运动以及混沌运动.     

Folding and unbinding transitions in tethered membranes

Molecular dynamics simulations of tethered membranes indicate that an attraction between the monomers leads to a well-defined sequence of folding transitions with decreasing temperature. With insights gained from Landau theory and simulations of bimembranes, the folding transitions are found to be intimately linked to the unbinding of membranes. Finite-size effects, mainly due to the loss of entropy from edge fluctuations, play an important role in hindering folding transitions.     

运用混沌理论制作长期灾害预报模型初探

为了提供准确的农业灾害预报，本研究运用混沌理论，以北京历年重大旱灾预报为例，构建了长期灾害混沌预报模型。该模型采用便于描绘混沌事件的三阶差分方程与多因子状态方程联立，模拟出北京市1955－2001年的历次旱灾事件发生过程。按照该模型规定的法则做重大旱灾预测比用单纯统计预测的准确率有显著提高。灾害混沌预报模型可作为长期灾害预测的新途径。     

Dynamics of conformational transitions in polymers

Conformational transitions in polymers involve large angle rotations about bonds. The process must proceed in a way that does not require gross movements of the macromolecules. The dynamics have been investigated by computer simulation and kinetic theory. The rate-determining step in the transition is found to occur in a mode which is kept local by distortion of nearby parts of the molecule. One especially important type of cooperativity, crank-like counterrotation of second-neighbor bonds, is identified. Experiments which provide evidence about the dynamics of conformational transitions are discussed.     

Evolutionary dynamics of biological games

Darwinian dynamics based on mutation and selection form the core of mathematical models for adaptation and coevolution of biological populations. The evolutionary outcome is often not a fitness-maximizing equilibrium but can include oscillations and chaos. For studying frequency-dependent selection, game-theoretic arguments are more appropriate than optimization algorithms. Replicator and adaptive dynamics describe short- and long-term evolution in phenotype space and have found applications ranging from animal behavior and ecology to speciation, macroevolution, and human language. Evolutionary game theory is an essential component of a mathematical and computational approach to biology.     

运用延迟反馈消除混沌的分析

以永磁电动机模型为例,研究如何运用延迟反馈来控制混沌。首先在理论上分析永磁电动机模型延迟反馈控制混沌的可行性,然后通过仿真实验验证其正确性。通过研究可知运用延迟反馈可以很好地消除混沌使系统达到一个稳定的状态。     

Chaos, strange attractors, and fractal basin boundaries in nonlinear dynamics

Recently research has shown that many simple nonlinear deterministic systems can behave in an apparently unpredictable and chaotic manner. This realization has broad implications for many fields of science. Basic developments in the field of chaotic dynamics of dissipative systems are reviewed in this article. Topics covered include strange attractors, how chaos comes about with variation of a system parameter, universality, fractal basin boundaries and their effect on predictability, and applications to physical systems.     

基于混沌理论的自适应模糊推理网络系统在径流时间序列预测中的应用

水文期预报对水资源管理、调度及社会的生产、生活具有十分重要的意义。针对常规混沌预测方法的局限性,提出基于混沌理论的自适应模糊推理网络系统的径流时间序列预报方法。该方法径流时间序列被分解为趋势项、周期项和随机项,对随机项进行混沌辨识,然后建立有自适应能力的神经网络模糊推理模型对随机项进行预测,最后将各项线性叠加进行径流预报。实例表明,该方法预测精度较高,具有良好的泛化推广能力。     

水平管内油气两相流型转变的实验研究

通过进行水平管内油气两相流型实验，对影响管内油气两相流型转换的各种因素进行了综合的分析，并根据所作的油气两相流型试验结果，用量纳分析的方法得出了各流型间转换的准则关系式，以期达到准确定量地预报水平及倾斜管中油气两相流型的目的。