Chaotic Scattering in the Restricted Three‐Body Problem II. Small mass parameters     

L. Benet  T. H. Seligman  D. Trautmann 《Celestial Mechanics and Dynamical Astronomy》1998,71(3):167-189

We study the scattering motion of the planar restricted three‐body problem for small mass parameters μ. We consider the symmetric periodic orbits of this system with μ = 0 that collide with the singularity together with the circular and parabolic solutions of the Kepler problem. These divide the parameter space in a natural way and characterize the main features of the scattering problem for small non‐vanishing μ. Indeed, continuation of these orbits yields the primitive periodic orbits of the system for small μ. For different regions of the parameter space, we present scattering functions and discuss the structure of the chaotic saddle. We show that for μ < μc and any Jacobi integral there exist departures from hyperbolicity due to regions of stable motion in phase space. Numerical bounds for μc are given. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

赤道东太平洋温度锋附近的混沌输运与混合     

姜华  吴德星  吕建 《中国海洋大学学报(自然科学版)》2002,32(2):165-172

运用 Mc Creary和 Yu(1992 )的非线性 2 12 层模式的积分流场 ,研究了混沌混合与输运对海水及要素浓度的输运和混合问题。模式结果显示混沌混合区主要分布于赤道东太平洋不稳定区及东、西边界附近 ,中西太平洋的大部分区域为非混沌区。释放在混沌区内的示踪团随时间的弥散过程要较非混沌区内的示踪团复杂的多。因多模态不稳定波动的共同作用 ,尤其是在赤道上经向运动最强的 Yanai波的加入 ,使得赤道不稳定区的流体以混沌混合的方式均匀地弥散开 ,趋向于粗粒 (coarse- grained)意义下的均匀化。并有大量释放于赤道东太平洋不稳定区的示踪质点越过赤道进入对面半球。背景辐散流的加入能将部分示踪点输送出混合区使其不加入均匀化过程 ,故最后混入另一半球的质点数少于半数。过赤道交换速率则主要由混沌混合的强度有关。  相似文献   

LOCALIZED FEATURES OF CHAOTIC SYSTEM AND ATMOSPHERIC PREDICTABILITY          下载免费PDF全文

Li Zhijin  Ji Liren 《Acta Meteorologica Sinica》1995,9(4):432-444

The localized features on chaotic attractor in phase space and predictability are investigated in thepresent study.It will be suggested that the localized features in phase space have to be considered indetermining the predictability.The notions of the local instability including the finite-time and local-time instabilities which determine the growth rate of error are introduced,and the calculation methodsare discussed in detail.The results from the calculation of the 3-component Lorenz model show thatsuch instability,correspondingly the growth rate of error,varies dramatically as the trajectoriesevolve on the chaotic attractor.The region in which the growth rate of error is small is localizedconsiderably,and is separable from the region in which the growth rate is large.The localpredictability is of important interest.It is also suggested that such localized features may be the maincause for a great deal of case-to-case variability of the predictive skill in the operational forecasts.  相似文献   

Is there an attractor for the Indian summer monsoon?     

V Satyan 《Journal of Earth System Science》1988,97(1):49-52

Aperiodicity in the time series of Indian summer rainfall for 116 years is analysed using the phase space approach. The question whether a low-dimensional strange attractor is associated with the chaotic behaviour of the monsoon system is investigated. It is found that a strange attractor of dimensionality around 5·1 exists and the system has 12 relevant degrees of freedom.  相似文献   

同相轴完整程度对混沌振子检测效果的影响     

袁野  罗正玮  李月 《世界地质》2006,25(1):91-94

针对地震勘探资料含加性强随机噪声,已提出用混沌振子系统检测同相轴的方法。就同相轴完整程度对系统检测效果影响进行研究表明,对于含有不同个数Ricker子波的同相轴,个数越多,同相轴可检测的速度分布带越大,越接近准确速度,系统检测SNR越好;对于不同截断长度的同相轴,可检测的最佳SNR均出现在准确速度上;同相轴长度一定的情况下,扫描速度相同时,同相轴起始道序号越小,检测SNR越好。  相似文献   

相空间重构中时滞判定的功率谱分析法   总被引：1，自引：0，他引：1  

刘传孝  谭云亮  秦广鹏  吴子科 《岩土力学》2004,25(Z1):83-86

从再现系统原始信息和确定混沌关键指标角度,论证了相空间重构中时滞判定的重要性。构建基于时滞的时间序列自相关系数和自相关函数式,提出了时滞判定的功率谱方法。通过实际应用效果的比较,时滞判定的功率谱方法具有数据处理量较小和判别过程较稳定的优点,在一定程度上解决了Wolf方法确定Lyapunov指数鲁棒性较差的问题。  相似文献   

Earthquake mechanism and predictability shown by a laboratory fault     

Chi-Yu King 《Pure and Applied Geophysics》1994,143(1-3):457-482

Slip events generated in a laboratory fault model consisting of a circulinear chain of eight spring-connected blocks of approximately equal weight elastically driven to slide on a frictional surface are studied. It is found that most of the input strain energy is released by a relatively few large events, which are approximately time predictable. A large event tends to roughen stress distribution along the fault, whereas the subsequent smaller events tend to smooth the stress distribution and prepare a condition of simultaneous criticality for the occurrence of the next large event. The frequency-size distribution resembles the Gutenberg-Richter relation for earthquakes, except for a falloff for the largest events due to the finite energy-storage capacity of the fault system. Slip distributions, in different events are commonly dissimilar. Stress drop, slip velocity, and rupture velocity all tend to increase with event size. Rupture-initiation locations are usually not close to the maximum-slip locations.  相似文献   

浑沌气候学研究进展   总被引：3，自引：0，他引：3  

王勤学  曹鸿兴 《地球科学进展》1993,8(4):1-10

对近几十年来兴起的动力气候模式作了全面的介绍和分析,指出气候系统是一类浑沌动力系统,具有对参数和初值的极其敏感性、内在随机性,以及自相似性等。Lorenz最先发现气候系统中的浑沌性质,之后Saltzman建立一系列简单的海洋、大气、海冰耦合的动力气候模式,通过对这些模式的试验研究,揭示了气候随太阳辐射、二氧化碳、气溶胶等参数的变化规律及其浑沌动力学性质。这些性质都表现在各种气候因子的时间序列中,为此,人们开始从时间序列中提取动力系统的演变信息,如计算分维数、Lyapunov指数以及建立相空间预报模式等。本文就上述问题的研究进展进行了全面的综述并作了展望。  相似文献   

基于多切换模式的多混沌系统有限时组合同步     

李超  张斌  陈向勇  李天择  董和夫 《南京气象学院学报》2019,11(4):435-439

本文研究了多切换模式下混沌系统的有限时同步控制问题.针对多个不同阶实变量混沌系统,研究了其多切换同步行为,给出了有限时多切换组合同步的定义,进而,在给出误差系统的基础上,设计了一类实现快速同步的有限时控制方案,并给出了误差系统有限时稳定的充分条件.最后,仿真结果表明所设计控制方案具有快速收敛性,较好地验证了有效性.  相似文献   

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朱玉  赵卿  梅艳 《大地测量与地球动力学》2012,32(5):53-57

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