用于检测同相轴的Duffing型系统恢复力项的讨论          下载免费PDF全文

赵雪平  李月  杨宝俊 《地球物理学进展》2006,21(1):61-69

在用于检测同相轴的Duffing型系统中,非线性恢复力项的选取至关重要.针对具有不同非线性恢复力项的混沌系统,本文首先就非线性恢复力项的来源进行了说明,通过对哈密顿系统和耗散系统的仿真实验分析,以及理论推导,确定了势能—哈密顿多项式方程中可用于混沌振子检测系统的各项幂次和各项系数组合关系,即非线性恢复力项的选取规则:幂次最高项为奇次,其系数大于零.  相似文献   

Chaotic behaviour in a low-order unforced,inviscid barotropic model     

Charles A. Lin  Bong H. Lian 《Pure and Applied Geophysics》1986,124(6):1087-1105

A low-order model of the unforced, inviscid barotropic model is examined as a dynamical system. Analytic solutions, consisting of linear and nonlinear oscillations (Rossby waves), are obtained in appropriate limiting initial conditions. These solutions are periodic. With less restrictive initial conditions the system shows quasi-periodic behaviour at low energies and chaotic behviour at high energies. This transition is accompanied by frequency-locking and period-doubling. Quasi-periodic and chaotic behaviour may coëxist in phase space for the same values of the model invariants. The results are interpreted in terms of perturbed integrable Hamiltonian systems. Considerations of the low-frequency variability of the atmosphere are also made.  相似文献   

Numerical results to the Sitnikov-problem     

R. Dvorak 《Celestial Mechanics and Dynamical Astronomy》1993,56(1-2):71-80

We present numerical results of the so-called Sitnikov-problem, a special case of the three-dimensional elliptic restricted three-body problem. Here the two primaries have equal masses and the third body moves perpendicular to the plane of the primaries' orbit through their barycenter. The circular problem is integrable through elliptic integrals; the elliptic case offers a surprisingly great variety of motions which are until now not very well known. Very interesting work was done by J. Moser in connection with the original Sitnikov-paper itself, but the results are only valid for special types of orbits. As the perturbation approach needs to have small parameters in the system we took in our experiments as initial conditions for the work moderate eccentricities for the primaries' orbit (0.33e _primaries 0.66) and also a range of initial conditions for the distance of the 3 ^rd body (= the planet) from very close to the primaries orbital plane of motion up to distance 2 times the semi-major axes of their orbit. To visualize the complexity of motions we present some special orbits and show also the development of Poincaré surfaces of section with the eccentricity as a parameter. Finally a table shows the structure of phase space for these moderately chosen eccentricities.  相似文献   

基于一类离散动力系统的混沌加密研究     

刘建生  傅惠 《华东地质学院学报》2003,26(2):136-138

研究了一类具有良好隐蔽性的一元三次离散动力系统的混沌序列产生情况，提出了混沌序列的异或和置乱加密算法。实验结果证明，该系统所生成的混沌序列有密钥复杂、安全性较高的特点，具有推广应用的价值。  相似文献   

古气候变化吸引子维数对比研究     

袁林旺  周春林  刘泽纯 《地理与地理信息科学》2002,18(3):94-96

对世界上不同地区的多条古气候曲线 ,采用相同的间距和同一种算法进行关联维数计算 ,结果表明各系统均具有非线性作用产生的混沌现象。与太阳辐射曲线关联维数对比表明 ,太阳辐射控制了气候变化的基本格局 ,在此基础上叠加了区域性特征。  相似文献   

A multi-spiral set of solutions of a 3-D Hamiltonian system     

B. Barbanis 《Celestial Mechanics and Dynamical Astronomy》1993,55(1):87-98

Various sets of periodic solutions of a 3-D Hamiltonian system crossing perpendicularly thez=0 plane are presented. These sets form a main multi-spiral pattern and two secondary ones which have three focal points. The main pattern is inside a stochastic region that surrounds a simple complex unstable periodic orbit, while the two secondary patterns are parts of a stochastic sea. Through these regions the stochastic region communicates with the stochastic sea.  相似文献   

A mapping for the study of the 1/1 resonance in a galactic type Hamiltonian     

N. D. Caranicolas 《Celestial Mechanics and Dynamical Astronomy》1989,47(1):87-96

We derive an algebraic mapping for an autonomous, two-dimensional galactic type Hamiltonian in the 1/1 resonance case. We use the mapping to study the stability of the periodic orbits. Using the x — p _x Poincaré surface section, we compare the results of the mapping with those found by the numerical integration of the full equations of motion. For small values of the perturbation the results of the two methods are in very good agreement while satisfactory agreement is obtained for larger perturbations.  相似文献   

对水文时间序列混沌特征参数估计问题的讨论   总被引：15，自引：0，他引：15       下载免费PDF全文

王文  许武成 《水科学进展》2005,16(4):609-616

水文过程到底是不是低维混沌过程一直是个有争议的问题。相关文献在混沌特征参数估计中存在不少问题,包括:时延量估计的主观性很强,不同研究者的估计值差别很大;在关联维估计中,很多研究者有意无意地忽略了一个基本原则,即只有在关联维估计图上存在明确的标度区的情况下才能准确判断存在有限关联维;很多研究者在计算水文时间序列的关联维时仍采用原始的G-P计算公式,而没有采用Theiler提的修正公式,从而可能误将相点在时序上的相关性当做一种状态空间几何特征,造成关联维估计错误;国内相关研究中还普遍存在序列长度偏短的问题,对这些问题进行了讨论并给出了相应的结论。  相似文献   

Equation of a Barotropic Fluid on a Rotating Spherical Surface and its Inertial Manifold     

J. Horák 《Studia Geophysica et Geodaetica》2000,44(1):26-37

The inertial manifold is a positive invariant set which exponentially attracts all the trajectories of a dissipative dynamic system. It was introduced for the purpose of studying the asymptotic behaviour of such systems. The initial infinitely dimensional dynamic system, generated by a partial differential evolution equation, can be projected on to it, in order to obtain the final system of ordinary differential equations (inertial equations). These equations then simulate the initial object. Although the inertial manifold is an object relatively simpler than the attractor (a very complicated set of non-integer dimension may be an attractor) it is more difficult to prove its existence than that of the attractor. The equation of a barotropic fluid on a rotating spherical surface is one of the examples of dissipative dynamic systems with an inertial manifold. This kindles the hope that also the equations of the dynamics of the real atmosphere will have an inertial manifold. The reduction of the sample system to this Lipschitz manifold of finite dimension thus justifies us in analysing the behaviour of the atmosphere on non-linear models of finite dimensions and few parameters, in a finite system of ordinary differential equations.  相似文献   

基于相空间重构的边坡位移预测   总被引：20，自引：1，他引：19  

周创兵  陈益峰 《岩土力学》2000,21(3):205-208

根据边坡位移时间序列的非线性性质, 应用基于相空间重构的实时预测方法, 可以充分利用时间序列信息, 预测 各种边坡变形演化趋势。 讨论了局域法和基于 Ly apunov 指数的预测法。 实例研究表明, 基于相空间重构的预测方法具 有比非平稳时间序列更高的预测精度和更广的适应性。  相似文献