Origin of chaos in the Prometheus-Pandora system

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting, resulting in resonance overlap which causes the chaos. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 and 3.1 deg yr⁻¹, respectively. A model with 1.5 degrees of freedom captures the essential features of the chaotic dynamics. We use it to show that the Lyapunov exponent of 0.3 yr⁻¹ arises because the critical argument of the dominant member of the resonant quartet makes approximately two separatrix crossings every 6.2 year precessional cycle.     

Dynamics of Two Planets in the 3/2 Mean-motion Resonance: Application to the Planetary System of the Pulsar PSR B1257+12

This paper considers the dynamics of two planets, as the planets B and C of the pulsar PSR B1257+12, near a 3/2 mean-motion resonance. A two-degrees-of-freedom model, in the framework of the general three-body planar problem, is used and the solutions are analyzed through surfaces of section and Fourier techniques in the full phase space of the system.On the possibility of existence of a fourth planet in distant orbit, see Wolszczan et al., 2000     

Frequency modified fourier transform and its application to asteroids

Recently a method has been suggested to analyze the chaotic behaviour of a conservative dynamical system by numerical analysis of the fundamental frequencies. Frequencies and amplitudes are determined step by step. As the frequencies are not generally orthogonal, a Gramm-Schmidt orthogonalization is made and for each new frequency the old amplitudes of previously determined frequencies are corrected. For a chaotic trajectory variations of the frequencies and amplitudes determined over different time periods are expected. The change of frequencies in such a calculation is a measure of the chaoticity of the trajectory. While amplitudes are corrected, the frequencies (once determined) are constant. We suggest here simple linear corrections of frequencies for the effect of other close frequencies. The improvement of frequency determination is demonstrated on a model case. This method is applied to the first fifty numbered asteroids.     

Extracting flow structures from tracer data

A method of visualizing structures in closed chaotic flows out of homogenous particle distributions is presented in the example of models of a meandering jet. To this end, the system will be leaked or opened up by defining a region of the flow, so that a particle is considered to be escaped if it leaves this region. By applying this method to an ensemble of nonescaped tracers, we are able to characterize mixing processes by visualizing the converging and stretching filamentations (stable and unstable manifolds) in the flow without using additional mathematical tools. The possibility of applying the algorithm to analyze buoy data, and a comparison with the finite time manifolds are discussed.     

Epistemological possibilities and imperatives of complexity research: a reply to Reitsma

Reitsma (A response to ‘simplifying complexity’. Geoforum 34 (1) (2003) 13), in response to the article ‘Simplifying Complexity’ (Manson, S.M., Simplifying complexity: a review of complexity theory. Geoforum 32 (3) (2001) 405), highlights a number of interesting and important aspects of complexity theory that invite further discussion. In particular, there are three areas of complexity research that are open to deeper exploration: (1) the width and breadth of ‘complexity’ defined as a scientific endeavor; (2) the role of theory relative to practice and their relationship with pattern and process in complex systems; and (3) the need for greater discussion and exploration in order to define the conceptual bounds of complexity theory.     

一种基于浑沌理论的联想记忆神经网络模型

根据联想记忆神经网络的基本原理，提出了一种基于浑沌理论的联想记忆神经网络模型及相应的求解方案，并对该种模型进行了预报试验。结果表明，该种模型的历史预报准确率和实际预报准确率均超过一般随机预报，值得进一步研究和应用。     

人地非线性相关作用的探讨

从自组织系统思想出发，提出了人地关系的基本特性，通过逻辑斯蒂听数学变换，分析了人地非线性相关作用的混沌特性，进而讨论了人地关系的分形性质。基于混 过程与分形结构的因果关系，指出：地球表层系统中的人文分形景观乃是人地非线性关系的混沌作用所致。     

Intermittent chaos in nonlinear wave–wave interactions in space plasmas

There is increasing observational evidence of nonlinear wave–wave interactions in space and astrophysical plasmas. We first review a number of theoretical models of nonlinear wave–wave interactions which our group has developed in the past years. We next describe a nonlinear three-mode truncated model of Alfvén waves, involving resonant interactions of one linearly unstable mode and two linearly damped modes. We construct a bifurcation diagram for this three-wave model and investigate the phenomenon of intermittent chaos. The theoretical results presented in this paper can improve our understanding of intermittent time series frequently observed in space and astrophysical plasmas.     

磁层顶等离子体中的混沌现象

本文研究了磁层顶等离子体的一个基本模型,得到了一新的非线性常微分方程组.数值分析表明,在一定的磁Reynolds数范围内,系统呈现混沌行为,相轨道趋向于奇异吸引子.     

分形与混沌理论在地震学中的应用与探讨

分形与混沌理论的研究与发展，揭示了自然界中一大类无规几何形体物理过程的内在规律性及其动力演化过程的内在随机性。这给我们探索自然界中分形客体的几何形态及其与内部物理本质的关系提供了一条暂新的途径。特别是这一理论给我们探讨地震问题，例如：探讨地震活动时空分布的确定性图像、地震演化过程的动力学行为、临界特征以及未来大地震的发生等问题，带来了某些希望。本文较详细地综述了近年来分形与混沌理论在地震学中的应用研究。全文共分５部分。第１部分是孕震过程的一般概述。第２部分描述单分形与多分形在地震学中的某些应用．文中第３部分介绍了混沌动力学中的某些研究在测震学与模型中的应用。第４部分综述了自组织临界现象和闪变噪声的研究．最后，第５部分是分形理论与混沌动力学在地球科学中的应用前景与展望．