Chaotic gravitational zones around a regularly shaped complex rotating body     

E. Mysen  Ø. Olsen  K. Aksnes 《Planetary and Space Science》2006,54(8):750-760

In preparation for the Rosetta mission, the location and widths of gravitational resonances surrounding a regularly shaped and possibly complex rotating body are mapped following the second fundamental model of resonance. It is found that for uniaxial rotation of the central body, the surrounding resonances are widest for prograde orbits. If the figure axis is tilted with respect to the spin axis of the central body, an additional number of wide resonances appear with a preference for prograde and inclined orbits, and the occurrence of initial conditions which lie in the globally connected chaotic web is significantly increased. For larger rotational excitations, it is seen how these new additional resonances overlap internally at low eccentricity for very large semi-major axes. However, with exceptions for some excited short-axis rotational modes of the central body, it is argued that most resonances vanish for retrograde orbits lying in the plane normal to the body spin, and that resonant or non-resonant stability therefore can be expected for a wide range of mean orbit eccentricities.  相似文献   

逻辑斯蒂模型及应用     

王力勤  彭白桦 《成都信息工程学院学报》1997,(4)

通过对逻辑斯蒂模型的讨论，采用灰色理论和二态逐步回归等方法进行建模，解决了在某些建模问题中估计与计算参数出现的困难，并将其应用于医学和人口问题取得了满意的结果。  相似文献   

Exploring the 7:4 mean motion resonance—II: Scattering evolutionary paths and resonance sticking     

Patryk Sofia Lykawka  Tadashi Mukai 《Planetary and Space Science》2006,54(1):87-100

In our preliminary study, we have investigated basic properties and dynamical evolution of classical TNOs around the 7:4 mean motion resonance with Neptune (a∼43.7 AU), motivated by observational evidences that apparently present irregular features near this resonance (see [Lykawka and Mukai, 2005a. Exploring the 7:4 mean motion resonance—I. Dynamical evolution of classical trans-Neptunian objects (TNOs). Space Planet. Sci. 53, 1175-1187]; hereafter “Paper I”). In this paper, we aim to explore the dynamical long-term evolution in the scattered disk (but not its early formation) based on the computer simulations performed in Paper I together with extra computations. Specifically, we integrated the orbital motion of test particles (totalizing a bit more than 10,000) placed around the 7:4 mean motion resonance under the effect of the four giant planets for the age of the Solar System. In order to investigate chaotic diffusion, we also conducted a special simulation with on-line computation of proper elements following tracks in phase space over 4-5 Gyr. We found that: (1) A few percent (1-2%) of the test particles survived in the scattered disk with direct influence of other Neptunian mean motion resonances, indicating that resonance sticking is an extremely common phenomenon and that it helps to enhance scattered objects longevity. (2) In the same region, the so-called extended scattered TNOs are able to form via very long resonance trapping under certain conditions. Namely, if the body spends more than about 80% of its dynamical lifetime trapped in mean motion resonance(s) and there is the action of a k+1 or (k+2)/2 mean motion resonance (e.g., external mean motion resonances with Neptune described as (j+k)/j with j=1 and 2, respectively). According to this hypothetical mechanism, 5-15% of current scattered TNOs would possess thus probably constituting a significant part of the extended scattered disk. (3) Moreover, considering hot orbital initial conditions, it is likely that the trans-Neptunian belt (or Edgeworth-Kuiper belt) has been providing members to the scattered disk, so that scattered TNOs observed today would consist of primordial scattered bodies mixed with TNOs that came from unstable regions of the trans-Neptunian belt in the past.Considering the three points together, our results demonstrated that the scattered disk has been evolving continuously since early times until present.  相似文献   

Analysis of Sunspot Activity Cycles     

Robert A. Greenkorn 《Solar physics》2009,255(2):301-323

A nonlinear analysis of the daily sunspot number for each of cycles 10 to 23 is used to indicate whether the convective turbulence is stochastic or chaotic. There is a short review of recent papers considering sunspot statistics and solar activity cycles. The differences in the three possible regimes – deterministic laminar flow, chaotic flow, and stochastic flow – are discussed. The length of data sets necessary to analyze the regimes is investigated. Chaos is described and a chronology of recent results that utilize chaos and fractals to analyze sunspot numbers follows. The parameters necessary to describe chaos – time lag, phase space, embedding dimension, local dimension, correlation dimension, and the Lyapunov exponents – are determined for the attractor for each cycle. Assuming the laminar regime is unlikely if chaos is not indicated in a cycle by the calculations, the regime must be stochastic. The sunspot numbers in each of cycles 10 to 19 indicate stochastic behavior. There is a transition from stochastic to chaotic behavior of the sunspot numbers in cycles 20, 21, 22, and 23. These changes in cycles 20 – 23 may indicate a change in the scale of turbulence in the convection zone that could result in a change in the convective heat transfer and a change in the size of the convection region for these four cycles.  相似文献   

Empirical evidences of persistence and dynamical chaos in solar–terrestrial phenomena     

S. Panchev  M. Tsekov   《Journal of Atmospheric and Solar》2007,69(17-18):2391

This paper presents a brief review of selected publications concerning dynamical chaos and persistence in various solar–terrestrial phenomena ranging from solar activity to climate dynamics. It draws attention to the advanced approaches known in many research areas (meteorology, hydrology, biology, economics, etc.), but not yet sufficiently used in solar–terrestrial physics. First, we introduce the concepts of dynamical (deterministic) chaos and fractional Brownian motion. Next, we discuss appropriate methods—fluctuation analysis and nonlinear time series analysis—for treatment of erratic time series based on these concepts. We outline some pitfalls and problems in the application of the discussed methods to empirical data. Finally, we present selected empirical evidence for persistence and dynamical chaos in solar activity, solar wind, magnetosphere and ionosphere, weather and climate systems.  相似文献   

Ecological and agricultural productivity indices and their dynamics in a sub-humid/semi-arid region from central Mexico   总被引：1，自引：0，他引：1  

W. Ritter Ortíz  E. Juregui Ostos  S. Guzmn Ruíz  A. Estrada Betancourt  H. Muoz Nava  J. Surez Snchez  Ma. del Carmen Corona Vargas 《Journal of Arid Environments》2004,59(4):675

Using precipitation data from a semi-arid region in the highlands of central Mexico, historical values of productivity are assessed. Production models based on climatic indices are discussed. An empirical rain simulation equation shows that it is possible to reproduce the expected values of productivity from observed ecosystems and agricultural yields. A graphical method is proposed to estimate intrinsic growth rate and maximum sustainable yield. Spatial rainfall variability induced by orographic effects, introduces a chaotic semicyclic behavior as expected in a logistic simulation equation. Resilience and predictable drought-productivity tendencies can also be derived from this model.  相似文献   

海-气耦合系统的非线性不稳定行为与年际气候变率     

赵南  张勤  丁一汇 《气象学报》2002,60(3):318-325

文中从理论上论述了气候系统的基本态—季节循环的非线性不稳定特征 ,研究了年际气候变率特别是ENSO与季节循环间非线性相互作用 ,并通过Oxford海 气耦合模式数值实验具体展示了上述理论分析。理论与数值实验表明 ,海 气耦合系统可经过年周期态失稳→新周期产生→与季节循环锁相→混沌这一系列分岔过程产生类似ENSO的无规则运动。这一规律为正确认识ENSO的动力机制及客观确定简化海 气耦合模式中的参数提供了理论依据  相似文献   

微弱方波信号检测模型混沌解的判定     

李月  杨宝俊  郭华 《地球物理学进展》2002,17(1):133-136

薄油气储层的识别和解释中存在极其微弱有效信号，对这些有效信号进行混沌检测的先决条件是检测模型存在混沌区域。本文以微弱方波有效信号为例，运用Melnikov方法就混沌检测模型（Dufing方程）的混沌判据问题进行数学,证明并推导该数学模型出现混沌状态的临界值，为薄油气储层的识别和解释中的微弱信号的混沌检测提供理论依据。  相似文献   

淮河流域洪涝变化动力系统研究   总被引：6，自引：3，他引：6  

周寅康  王腊春  许有鹏  张捷 《地理科学》2001,21(1):41-45

非线性现象是现代科学最重要的研究课题之一，地理现象无不存在着非线性，目前，地理学对非线性现象的研究多从分形角度开展，对其本质－混沌的研究较少，在先前关于淮河流域洪涝变化序列及其非线性特征研究的基础上，运用混沌理论和微分议程理论，对淮河流域洪涝变化混沌动力系统进行了初步研究，重建了一个3维2次非线性模型，研究表明，淮河流域洪涝变化混沌动力系统具有较Lorenz等典型混沌系统更复杂的形式。  相似文献   

耗散结构混沌分形等新理论在地质学研究中的应用   总被引：5，自引：0，他引：5  

秦葆瑚 《湖南地质》1994,13(4):241-249

地球各圈层充满了复杂性与千奇百怪的变比，难以捉摸。而经典的数学公式，物理和化学定律，都只能用来从事最简单事物的研究，把它们用到地质学研究的复杂环境中去就无法适应了。近年来耗散结构理论，混沌运动与分形科学的发展，提供了研究复杂事物的科学方法，特别适合地质学研究的需要。本文对这些新理论作了简要介绍，希望能起到拓宽地质学研究思路的作用。  相似文献