The origin of chaotic behaviour in the Miranda-Umbriel 3 : 1 resonances     

Jacques Henrard  Massae Sato 《Celestial Mechanics and Dynamical Astronomy》1989,47(4):391-417

We have investigated the pericentric resonances through which Miranda and Umbriel are believed to have passed when, due to tidal evolution, their orbital mean motions reached a 3 : 1 commensurability. Our investigation is based upon a perturbative treatment. The predictions of this theory are in good agreement with the results of numerical integrations concerning both the extend of the chaotic layers generated by the separatrices of the primary resonances and the location of the secondary resonances. The effect of tidal evolution is discussed on the bases of the adiatatic invariant theory and its extension to separatrix crossing. We recover qualitatively the mean features of the numerical experiments of Tittermore and Wisdom (1988–1989), Dermott et al (1988) and Malhotra and Dermott (1989).  相似文献   

Complexity Theory of Natural Disasters; Boundaries of Self-Structured Domains     

Scheidegger  A. E. 《Natural Hazards》1997,16(2-3):103-112

Disasters are often represented as complete breakdowns of quasi-stationary states in a landscape, but may also be part of the normal evolution of such states. A landscape is, in fact, an open, nonlinear, dynamic system where the tectonic uplift and the seismic activity represent the input, the mass wastage and the relief degradation the output. The apparent 'stability' is due to the fact that open, nonlinear dynamic systems tend to develop into relatively stable, self-organized ordered states 'at the edge of chaos', with a fractal attractor. Short of complete breakdown, such systems re-establish order in steps of various magnitudes which have a power-law distribution. Because of the fractal structure of the basic attractor, all subsets follow a power law which accounts for the distribution of the steps of recovery. As the domains of quasi-stationarity at the edge of chaos are represented by finite windows, the power-law does not cover all magnitudes. The stationarity windows are not only limited in range, but also in space and time. This should be taken into account in the assessment of hazards. Examples are given from seismology (earthquake frequency), volcanology (eruption frequency), river hydrology (flood frequency) and geomorphology (landslides).  相似文献   

Regular and Chaotic Solutions of the Sitnikov Problem near the 3/2 Commensurability     

M. A. Jalali  S. H. Pourtakdoust 《Celestial Mechanics and Dynamical Astronomy》1997,68(2):151-162

Regular solutions at the 3/2 commensurability are investigated forSitnikovs problem. Utilizing a rotating coordinate system and theaveraging method, approximate analytical equations are obtained for thePoincare sections by means of Jacobian elliptic functions and 3periodicsolutions are generated explicitly. It is revealed that the system exhibitsheteroclinic orbits to saddle points. It is also shown that chaotic regionemerging from the destroyed invariant tori, can easily be seen for certaineccentricities. The procedure of the current study provides reliable answersfor the long-time behavior of the system near resonances.  相似文献   

遗传算法改进的BP神经网络在混沌径流时间序列预测中的应用     

刘媛媛  练继建  朱云 《水文》2007,27(2):45-48

区别于传统的提取混沌时间序列饱和嵌入维数的方法,本文利用人工神经网络成功地对水库混沌径流时间序列的饱和嵌入维数进行了提取,计算了该时间序列里的最大Lyapunov指数,两种方法结果都证明了该时间序列的混沌性。并用遗传算法对BP神经网络进行了改进,利用该模型对三门峡水库混沌径流时间序列进行了预测。实例计算表明该方法解决了BP神经网络收敛速度慢和易于陷入极小值的问题,大大提高了BP神经网络的计算精度和收敛速度。无论在计算精度上还是在收敛次数上都优于没有改进的BP神经网络。  相似文献   

Experimental and theoretical simulations of seismic poundings between two adjacent structures     

K. T. Chau  X. X. Wei  X. Guo  C. Y. Shen 《地震工程与结构动力学》2003,32(4):537-554

Shaking table tests have been carried out to investigate the pounding phenomenon between two steel towers of different natural frequencies and damping ratios, subject to different combinations of stand‐off distance and seismic excitations. Both harmonic waves and ground motions of the 1940 El Centro earthquake are used as input. Subjected to sinusoidal excitations, poundings between the two towers could appear as either periodic or chaotic. For periodic poundings, impact normally occurs once within each excitation cycle or within every other excitation cycle. A type of periodic group poundings was also observed for the first time (i.e. a group of non‐periodic poundings repeating themselves periodically). Chaotic motions develop when the difference of the natural frequency of the two towers become larger. Under sinusoidal excitations, the maximum relative impact velocity always develops at an excitation frequency between the natural frequencies of the two towers. Both analytical and numerical predictions of the relative impact velocity, the maximum stand‐off distance, and the excitation frequency range for pounding occurrences were made and found to be comparable with the experimental observations in most of the cases. The stand‐off distance attains a maximum when the excitation frequency is close to that of the more flexible tower. Pounding appears to amplify the response of the stiffer structure but suppress that of the more flexible structure; and this agrees qualitatively with previous shaking table tests and theoretical studies. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

COMPLEXITY AND CHAOTIC DYNAMICS OF ROCK FAULTING   总被引：1，自引：0，他引：1  

TANKaixuan XIEYanshi CHENGuanghao HUANGXiaonai 《大地构造与成矿学(英文版)》2003,27(1):104-111

Fault is a complex dynamic system controlled by the coupling of rock texture, reaction, fluid flow, stress, and rock deformation mechanism. A coupled reaction-transport- mechanical dynamic model for fault system is established and described in this paper. An example is presented for the Shuikoushan deposit, Hunan. The results of dynamic simulation indicate that the evolution and magnitude of fracture permeability of different rocks are different, and that faulting can enhance the spatial heterogeneity of rock permeability and facilitate fluid flow and mineralization in local fault zone. The pressure for a fault usually shows a variation mode of aperiodic oscillation with time, which reflects the chaotic behavior of the evolution of a fault.  相似文献   

An Analytic Model of Three-Body Mean Motion Resonances     

D. Nesvorný  A. Morbidelli 《Celestial Mechanics and Dynamical Astronomy》1998,71(4):243-271

It has been recently shown that the resonances among the mean motions of an asteroid, Jupiter and Saturn are very important for the origin of chaos in the asteroid belt. We develop an analytic model for these three-body resonances which allows quantitative predictions on their amplitude and libration timescale. We also discuss why these resonances are chaotic. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

流域降雨径流时间序列的混沌识别及其预测研究进展   总被引：38，自引：2，他引：38       下载免费PDF全文

黄国如  芮孝芳 《水科学进展》2004,15(2):255-260

混沌和随机在本质上是两种不同的特征,对这两种特征的描述方法各不相同,确定流域降雨径流时间序列的混沌性和随机性是对其进行模拟和预测的重要基础。近10多年来,许多学者相继开展了流域降雨径流时间序列的混沌识别及其预测研究。着重回顾其中最为重要的相空间重构、混沌识别和混沌预测方法,对将混沌理论应用于降雨径流时间序列的限制条件(序列的数据量大小和数据噪声)也进行了探讨。  相似文献   

Strange attractors in magmas: evidence from lava flows     

G. Poli  D. Perugini 《Lithos》2002,65(3-4):287-297

Magma mixing structures from three different lava flows (Salina, Vulcano and Lesbos) are studied in order to assess the possible chaotic origin of magma mixing processes. Structures are analysed using a new technique based on image analysis procedures that extract time series that are representative of the relative change in composition through the structures. These time series are then used to reconstruct the attractors underlying the magma mixing process and to calculate the fractal dimension of the attractors. Results show that attractors exist and possess fractional dimensions. This evidence suggests that the mixing of magmas is a chaotic process governed by a low number of degrees of freedom. In addition, fractal dimension analyses allows us to discriminate between different regimes of mixing in the three lava flows. In particular our analyses suggest that the lava flow of Salina underwent more turbulent mixing than the lava flows of Lesbos and Vulcano.  相似文献   

湘西金矿含矿石英脉厚度变化的分形和混沌分析   总被引：3，自引：3，他引：3  

谢焱石  谭凯旋  赵志忠 《大地构造与成矿学》2002,26(1):62-68

本文对湘西金矿主要矿脉的厚度变化进行了分形分析。各矿脉的厚度变化均具有分形结构特征,其中V1脉的分维值最小,V4脉的分维值最大;并且同一条矿脉在不同中段的分维值也有较大变化。通过对矿脉厚度变化的相空间重构,表明各矿脉厚度空间变化序列均为混沌演化序列,在相空间维数达到6～7时出现混沌吸引子,混沌吸引子的分维值为1.2～6.0。矿脉厚度变化的分维值越小,矿脉的平均厚度越大,其构造和流体活动也越强烈。构造变形、流体活动、矿物沉淀与岩石渗透率之间的非线性耦合作用以及矿脉通过连通而生长是导致矿脉厚度分形分布与混沌演化的主要动力学机理。  相似文献