给定参数条件下海温脉动随机模式的混沌行为     

严绍瑾  彭永清 《热带气象学报》1995,11(4):365-369

从Ｓａｌｔｚｍａｎ海气随机气候模式出发，得到了海温脉动θ＇的Ｌａｎｇｅｖｉｎ方程以及对应的Ｆｏｋｋｅｒ－ｐｌａｎｋ方程。在给定参数条件下求数值解，得到的概率密度曲线ｐ（ｘ，ｔ）具有多个极大值，并在ｐ（ｘ，ｔ）－ｐ（ｘ，ｔ＋τ）相空间中呈现Ｃａｎｔｏｒ集合图象，表明该随机系统在上述参数条件下出现了混沌行为。  相似文献   

非线性动力系统理论与地貌学研究   总被引：1，自引：0，他引：1  

郭跃 《地球科学进展》1995,10(6):605-611

非线性动力系统理论及其基本概念迅速地向地貌领域渗透和发展，使得愈来愈多的地貌学家运用ＮＤＳ的知识结构和思维方式认识地貌现象和地貌发展，许多地貌系统在时空上都显示出非线性或混沌的行为和方式。这些复杂性可能是地貌系统的不平衡、组成的多样和外界环境的变的结果。  相似文献   

地震道的非线性混沌反演——Ⅰ.理论和数值试验   总被引：32，自引：5，他引：32       下载免费PDF全文

杨文采 《地球物理学报》1993,36(2):222-232

全文以地震道反演的数值实验为例,根据混沌理论讨论了非线性地震反演的以下特性:1.对于带误差的地震数据和极其平滑的初始模型,逐次线性化的迭代过程产生的输出序列最终走向无序,这是非线性反演系统本身的特性决定的;2.迭代（非线性反演）系统是由Poin-care映的或系统方程描述的;3.可以根据地震反问题的特点,用多种不同的方法定义相应的Lyapunov指数,它们的数值和组合是非线性反演系统状态的有效指示;4.取决于系统参数的选取,发现在二维相空间有奇异吸引子的对应物.总之,从混沌理论的角度来研究纯数学的非线性地震反问题,可以揭示某些过去鲜为人知的内在规律性.本文为全文的上篇,主要讨论前两个问题,即理论和地震道反演数值试验结果.  相似文献   

Deterministic uncertainty in landscapes     

Jonathan D. Phillips 《地球表面变化过程与地形》1994,19(5):389-401

Deterministic complexity (chaos) may be common in geomorphic systems, but traditional definitions may have limited practical utility for empirical geomorphology. These definitions are based on sensitivity to initial conditions, which in geomorphology are both unknown and unknowable. Further, chaos analysis depends on distinguishing deterministic complexity from stochastic complexity. This is problematic in geomorphology because some stochastic complexity is virtually always present in addition to any chaos that may be present. While it is important to recognize that some complex, apparently random patterns may derive from inherent non-linear system dynamics, this is of limited use in explaining process–response relationships or mechanics of landscape evolution. A more general term, which subsumes chaos, is deterministic uncertainty, i.e. uncertainty associated with an identifiable but unknown or uncertain source. An analysis of landscape entropy shows that such underlying constraints produce spatial patterns which are apparently chaotic. For the case of geologic controls, the apparent contribution of deterministic chaos to the landscape entropy is a direct non-linear function of the extent of geologic constraints. However, the underlying constraints and their contribution to observed spatial patterns can also be interpreted in non-chaotic terms. Examples are given, involving geologic constraints on stream channel networks and parent material control of surface soil textures. Because both randomness and chaos may be more apparent than real, the concept of deterministic uncertainty is more useful in process geomorphology than that of chaos.  相似文献   

One to One Resonance at High Inclination     

R. Brasser  D. C. Heggie  S. Mikkola 《Celestial Mechanics and Dynamical Astronomy》2004,88(2):123-152

We report results from long term numerical integrations and analytical studies of particular orbits in the circular restricted three-body problem. These are mostly high-inclination trajectories in 1 : 1 resonance starting at or near the triangular Lagrangian L₅ point. In some intervals of inclination these orbits have short Lyapunov times, from 100 to a few hundred periods, yet the osculating semi-major axis shows only relatively small fluctuations and there are no escapes from the 1 : 1 resonance. The eccentricity of these chaotic orbits varies in an erratic manner, some of the orbits becoming temporarily almost rectilinear. Similarly the inclination experiences large variations due to the conservation of the Jacobi constant. We studied such orbits for up to 10⁹ periods in two cases and for 10⁶ periods in all others, for inclinations varying from 0° to 180°. Thus our integrations extend from thousands to 10 million Lyapunov times without escapes of the massless particle. Since there are no zero-velocity curves restricting the motion this opens questions concerning the reason for the persistence of the 1 : 1 resonant motion. In the theory sections we consider the mechanism responsible for the observed behavior. We derive the averaged 1 : 1 resonance disturbing function, to second order in eccentricity, to calculate a critical inclination found in the numerical experiment, and examine motion close to this inclination. The cause of the chaos observed in the numerical experiments appears to be the emergence of saddle points in the averaged disturbing potential. We determine the location of several such saddle points in the (, ) plane, with being the mean longitude difference and the argument of pericentre. Some of the saddle points are illustrated with the aid of contour plots of the disturbing function. Motion close to these saddles is sensitive to initial conditions, thus causing chaos.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

磁层顶磁岛结构及其非线性行为          下载免费PDF全文

王宪民  濮祖荫 《地球物理学报》1996,39(1):7-16

解析研究了磁层顶磁岛结构时间演化的非线性过程；推导出磁岛宽度的解析式和磁岛发生分叉、混沌的条件；论证了磁重联生成的磁岛有不稳定平衡结构，外扰作用会破坏该结构，使磁岛出现突变和混沌；说明了中小尺度太阳风脉动易使磁岛破碎，导致磁场湍动重联，形成小尺度结构．  相似文献   

混沌动力学及其在干旱预测中的应用   总被引：2，自引：0，他引：2  

罗哲贤  马镜娴 《干旱气象》1997,(3)

本文叙述了混沌动力学产生的科学背景，混沌动力学的基本概念，以及基于混沌动力学的干旱预测的技术方法。  相似文献   

火山震动特征及其动力学研究进展     

安镇文  叶正仁 《地震地磁观测与研究》1997,18(1):9-17

结合国内外资料，介绍了近年来火山震动的非线性动力学研究进展，并且讨论了预测火山活动的某些综合方法。  相似文献   

非线性地震道的混沌反演——Ⅱ.关于Lyapunov指数和吸引子   总被引：3，自引：0，他引：3  

杨文采 《地球物理学报》1993,(3)

在本文上篇《非线性地震道的混沌反演——1.理论和数值试验》中讨论了非线性反问题逐次线性化方法及迭代过程的系统特性、递推法和广义线性反演法输出波阻抗序列的特征。本篇参照混沌理论中关于Lyapunov指数、相空间和吸引子的概念,深入研究逐次线性化迭代的状态变化的阶段性及其定量描述.当引用相空间描述系统的演化时,对于随迭代变化的阻尼因子可以发现几种吸引子.最后,总结了非线性地震混沌反演的要点,指出非线性反演迭代的复杂阶段性要川混沌理论来描述,而Lyapunov指数等才是控制迭代过程的实质性参数.  相似文献   

The structure of chaos in a potential without escapes     

G. Contopoulos  H. Papadaki  C. Polymilis 《Celestial Mechanics and Dynamical Astronomy》1994,60(2):249-271

We study the structure of chaos in a simple Hamiltonian system that does no have an escape energy. This system has 5 main periodic orbits that are represented on the surface of section by the points (1)O(0,0), (2)C ₁,C ₂(±y _c, 0), (3)B ₁,B ₂(O,±1) and (4) the boundary . The periodic orbits (1) and (4) have infinite transitions from stability (S) to instability (U) and vice-versa; the transition values of are given by simple approximate formulae. At every transitionS U a set of 4 asymptotic curves is formed atO. For larger the size and the oscillations of these curves grow until they destroy the closed invariant curves that surroundO, and they intersect the asymptotic curves of the orbitsC ₁,C ₂ at infinite heteroclinic points. At every transitionU S these asymptotic curves are duplicated and they start at two unstable invariant points bifurcating fromO. At the transition itself the asymptotic curves fromO are tangent to each other. The areas of the lobes fromO increase with ; these lobes increase even afterO becomes stable again. The asymptotic curves of the unstable periodic orbits follow certain rules. Whenever there are heteroclinic points the asymptotic curves of one unstable orbit approach the asymptotic curves of another unstable orbit in a definite way. Finally we study the tangencies and the spirals formed by the asymptotic curves of the orbitsB ₁,B ₂. We find indications that the number of spiral rotations tends to infinity as . Therefore new tangencies between the asymptotic curves appear for arbitrarily large . As a consequence there are infinite new families of stable periodic orbits that appear for arbitrarily large .  相似文献