不确定混沌系统的反同步与参数辨识     

李农  李建芬  刘宇平 《海洋学报》2010,32(9):5954-5958

针对一类混沌系统,提出了一种系统的混沌反同步设计方案,基于该方案,设计一种自适应控制方法,实现了参数不确定系统的混沌反同步和未知参数的辨识.数值模拟结果表明了提出方法的有效性.  相似文献   

混沌系统的变结构同步控制     

李自强  唐功友  李娟 《中国海洋大学学报(自然科学版)》2009,39(3)

研究Lorenz混沌系统的同步控制问题,提出1种在多输入的情况下实现混沌同步的变结构控制算法.利用该算法设计的变结构同步控制律使得同步误差系统的运动在切换面上成为渐近稳定的滑动模态,从而较快的实现了混沌同步.通过对 Lorenz 混沌系统的理论分析和数值仿真,说明了该变结构同步控制策略的实用性和有效性.  相似文献   

Nonlinear Dynamic Behavior of Moored Buoy Excited by Free Surface Waves     

常宗瑜  徐长密  李华军  唐原广  张喜超 《中国海洋工程》2009,23(3):585-592

In this paper, studied are the dynamics of a moored buoy near the surface subjected to wave excitation. According to the physical structure, submersible buoy moored by tethered line is modeled firstly. Then from the differential equations, the natural frequencies are estimated by neglecting the coupling between tangential and normal direction. By use of numerical integration method, solutions are obtained. On this basis, strange attractors and bifurcation phenomena are obtained by applying Poincare map, pha...  相似文献   

Evidence of chaos in the rainfall-runoff process     

BELLIE SIVAKUMAR  RONNY BERNDTSSON  JONAS OLSSON  KENJI JINNO 《水文科学杂志》2013,58(1):131-145

Abstract

The transformation of rainfall into runoff is one of the most important processes in hydrology. In the past few decades, a wide variety of automated or computer-based approaches have been applied to model this process. However, many such approaches have an important limitation in that they treat the rainfall-runoff process as a realization of only a few parameters of linear relationships rather than the process as a whole. What is required, therefore, is an approach that can capture not only the overall appearance but also the intricate details of the nonlinear behaviour of the process. The purpose of this study is to investigate the possibility of understanding the dynamics of the rainfall-runoff process from a new perspective, as a chaotic process. The possible existence of chaotic behaviour in the rainfall-runoff process is studied by investigating the rainfall and runoff time series: (a) separately; and (b) jointly (using the runoff coefficient). Monthly rainfall and runoff observed over a period of 131 years (January 1807-December 1937) at the Göta River basin in the south of Sweden are analysed. The correlation dimension method is employed to identify the presence of chaos. The correlation dimensions obtained for the rainfall and runoff time series are 6.4 and 5.5, respectively. The finite dimensions obtained for the rainfall and runoff time series indicate the possible existence of chaos in these processes, implying that the joint rainfall-runoff process might also exhibit chaotic behaviour. The correlation dimension of about 7.8 obtained for the runoff coefficient also indicates the possible presence of chaos and supports the above results.  相似文献   

带电测试粒子在磁化史瓦西黑洞中的混沌运动          下载免费PDF全文

周娜英  张洪星  孙鑫  刘文芳  李丹 《天文学报》2023,64(4):39

当史瓦西黑洞周围存在渐近均匀的外部磁场时, 描述带电粒子在史瓦西黑洞附近运动的哈密顿系统会变为不可积系统. 类似于这样的相对论哈密顿系统不存在有显式分析解的2部分分离形式, 给显式辛算法的构建和应用带来困难. 近一年以来的系列工作提出将相对论哈密顿系统分解为具有显式分析解的2个以上分离部分形式, 成功解决了许多相对论时空构建显式辛算法的难题. 最近的工作回答了哈密顿系统显式可积分离数目对长期数值积分精度有何影响、哪种显式辛算法有最佳长期数值性能这两个问题, 指出哈密顿有最小可积分离数目即3部分分裂解形式并且应用于优化的4阶分段龙格库塔显式辛算法可取得最好精度. 由此选择上述数值积分方法并利用庞加莱截面、最大李雅普诺夫指数和快速李雅普诺夫指标研究在磁化史瓦西黑洞附近运动的带电粒子轨道动力学. 结果显示: 针对某特定的粒子能量和角动量, 较小的外部磁场很难形成混沌轨道; 较大的正磁场参数容易使轨道产生混沌, 并且随着磁场的增大, 轨道的混沌程度也随之加强; 粒子能量适当变大也可以加剧混沌程度, 但负磁场参数和粒子角动量变大都会减弱混沌.  相似文献   

地闪不规则先导的多尺度熵特征   总被引：2，自引：2，他引：0       下载免费PDF全文

李婵  张阳  吕伟涛  郑栋  谭涌波 《应用气象学报》2014,25(3):347-353

针对不规则脉冲簇难以判别问题,将多尺度熵应用于不规则先导分析中,探讨闪电信号不规则脉冲分析应用中多尺度熵关键参量的选择方法。在此基础上,将不规则先导与直窜先导及梯级先导闪电信号的多尺度熵进行比较。统计分析表明:不规则先导和直窜先导熵值随尺度先增加后趋于平稳,但熵值有很大差异;梯级先导熵值随尺度变化不明显,整体呈增长趋势,与不规则先导的熵值在大于3的尺度上也有所差异,因此当尺度大于3时可将熵值大于1.5的先导归类为不规则先导,熵值小于1.5的先导归类为梯级先导或直窜先导。不规则先导的特征熵平均值为2.0~2.1,最大值范围为2.6~2.8,最小值范围为1.51~1.59。  相似文献   

Phase Mixing in Unperturbed and Perturbed Hamiltonian Systems     

Henry E. Kandrup  Steven J. Novotny 《Celestial Mechanics and Dynamical Astronomy》2004,88(1):1-35

This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic driving, friction, and/or white and coloured noise. The evolution of initially localised ensembles of orbits was probed through lower order moments and coarse-grained distribution functions. In the absence of time-dependent perturbations, regular ensembles disperse initially as a power law in time and only exhibit a coarse-grained approach towards an invariant equilibrium over comparatively long times. Chaotic ensembles generally diverge exponentially fast on a time scale related to a typical finite time Lyapunov exponent, but can exhibit complex behaviour if they are impacted by the effects of cantori or the Arnold web. Viewed over somewhat longer times, chaotic ensembles typical converge exponentially towards an invariant or near-invariant equilibrium. This, however, need not correspond to a true equilibrium, which may only be approached over very long time scales. Time-dependent perturbations can dramatically increase the efficiency of phase mixing, both by accelerating the approach towards a near-equilibrium and by facilitating diffusion through cantori or along the Arnold web so as to accelerate the approach towards a true equilibrium. The efficacy of such perturbations typically scales logarithmically in amplitude, but is comparatively insensitive to most other details, a conclusion which reinforces the interpretation that the perturbations act via a resonant coupling.  相似文献   

Chaotic Orbits in Galactic Satellites     

D. D. Carpintero  J. C. Muzzio  M. M. Vergne  F. C. Wachlin 《Celestial Mechanics and Dynamical Astronomy》2003,85(3):247-267

In several previous papers we had investigated the orbits of the stars that make up galactic satellites and found that many of those orbits were chaotic. In those investigations we made extensive use of the frequency analysis method of Carpintero and Aguilar (1998) to classify the orbits, because that method is much faster than the use of Lyapunov exponents, allows the classification of the regular orbits and our initial comparison of both methods had shown excellent agreement between their results. More recently, we have found some problems with the use of frequency analysis in rotating systems, so that here we present a new investigation of orbits inside galactic satellites using exclusively Lyapunov exponents. Some of our previous conclusions are confirmed, while others are altered. Besides, the Lyapunov times that are now obtained show that the time scales of the chaotic processes are shorter than, or comparable to, other time scales characteristic of galactic satellites.  相似文献   

on the relationship between fast lyapunov indicator and periodic orbits for symplectic mappings     

Elena Lega  Claude Froeschlé 《Celestial Mechanics and Dynamical Astronomy》2001,81(1-2):129-147

The computation on a relatively short time of a quantity, related to the largest Lyapunov Characteristic Exponent, called Fast Lyapunov Indicator allows to discriminate between ordered and weak chaotic motion and also, under certain conditions, between resonant and non resonant regular orbits. The aim of this paper is to study numerically the relationship between the Fast Lyapunov Indicator values and the order of periodic orbits. Using the two-dimensional standard map as a model problem we have found that the Fast Lyapunov Indicator increases as the logarithm of the order of periodic orbits up to a given order. For higher order the Fast Lyapunov Indicator grows linearly with the order of the periodic orbits. We provide a simple model to explain the relationship that we have found between the values of the Fast Lyapunov Indicator, the order of the periodic orbits and also the minimum number of iterations needed to obtain the Fast Lyapunov Indicator values.  相似文献   

FAST LYAPUNOV INDICATORS. APPLICATION TO ASTEROIDAL MOTION     

CLAUDE FROESCHLÉ  ELENA LEGA  ROBERT GONCZI 《Celestial Mechanics and Dynamical Astronomy》1997,67(1):41-62

We present a very simple and fast method to separate chaotic from regular orbits for non-integrable Hamiltonian systems. We use the standard map and the Hénon and Heiles potential as model problems and show that this method appears to be at least as sensitive as the frequency-analysis method. We also study the chaoticity of asteroidal motion. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献