共查询到20条相似文献,搜索用时 109 毫秒
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一、引言 混沌是非线性系统在远离平衡状态下,由于运动轨迹高度不稳定经多次分岔达到的一种运动状态,是一种有统计规律的序.哈肯曾指出:“混沌性来源于决定论性方程的无规则运动.”那么确定论系统又是如何产生混沌的呢?由自然界中广泛存在的混沌现象,我们可以知道系统产生混沌归咎于非线性条件.单摆是物理学中的一个简单模型,是确定论的典型例子,但在有阻尼的情况下,受周期性驱动力作用之后,其运动规律就将发生变化,出现周期的分岔,在一定大小的驱动力条件下出现混沌行为.为了将这一由确定论走向混沌的全过程完整地演示出来… 相似文献
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考虑赝势近似下囚禁于Paul阱中的单离子与由脉冲式双激光驻波构成的棘齿势场的相互作用.应用积分方程方法得到系统的经典运动精确解,通过数值方法作出相空间轨道并计算由平均速度定义的流,结合分析与数值结果研究囚禁离子的规则与混沌运动特性.与单驻波型激光脉冲情形相比,发现两个重要的棘齿效应:一是脉冲式棘齿势场的作用导致参数空间混沌区域的改变,从而适当调节第二驻波参数,可使离子的规则运动变为混沌运动,或者混沌运动变为规则运动;二是通过分析平均流随激光参数的变化,发现棘齿势场的介入能使囚禁离子作平均意义下的单向输运,随着势场强度增加到混沌区域,流的强度明显减小并改变方向,系统进入混沌运动.
关键词:
脉冲式棘齿势
囚禁离子
混沌
输运 相似文献
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研究了有界噪声与谐和激励作用下的Duffing-Rayleigh振子的动力学行为.首先运用随机Melnikov过程方法得到系统出现混沌的条件,结果表明随着非线性阻尼参数的增加系统会从混沌运动到周期运动,随着Wiener过程强度参数的增加,系统由混沌进入周期的临界幅值会先递增后不变.最后,用两类数值方法即最大Lyapunov指数与Poincare截面验证了上述结果.
关键词:
有界噪声
随机Melnikov过程
混沌运动
周期运动 相似文献
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本文在实验教学中引入一种非线性混沌摆系统,通过调节混沌摆的驱动力周期演示了该非线性动力学系统出现混沌现象的过程,从而让学生了解混沌现象的参数敏感性、相图特点、频谱特性等基本特性.为了进一步了解该混沌摆的特性,本文建立了该非线性摆系统的简化动力学方程,在数值上对其进行了研究.基于动力学方程的数值模拟,克服了实验上相关参数定量改变困难、摆动稳定性不易控制、实验时间周期长等问题.在数值模拟中,通过改变不同参数得到了相图、频谱图以及分岔图,比较深入详细地对这种混沌摆的相关特性进行了描述,也有利于学生加深对混沌摆的理解. 相似文献
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This paper presents a numerical study of an autoparametric system composed of two elements: a pendulum and an excited nonlinear oscillator. Owing to an inertial coupling between the two elements, different types of motion are possible, from periodic to chaotic. This study examines a linear induction of an energy harvester depending on the pendulum motion. The harvester consists of a cylindrical permanent magnet mounted on a rotor and of four windings fixed to the housing as a stator. When the pendulum is rotating or swinging, the converter is generating energy due to magnetic induction. In this paper, a method utilizing parametrical resonance for harvesting energy from low frequency vibrations is studied. The authors compare energy induced by different types of pendulum motion: swinging, rotation and chaotic dynamics. Additionally, voltage values for different parameters of excitation are estimated. 相似文献
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依据非线性动力学混沌理论,采用受外力驱动的转动马达装置,依托PASCO系统的数据采集软件,开发了适应大学物理实验的受外力驱动的混沌摆实验。探讨了新型基于外力驱动的混沌摆实验仪在研究混沌效用上的应用,实验发现利用该装置可以直观的研究系统的初值敏感性,奇异子现象等,操作简单、直观、灵敏度高,实验除了具有实际应用价值外,同时适合在高等学校大学物理基础实验中开设出相应的实验教学内容。 相似文献
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Dynamical systems with nonlinear damping show interesting behavior in the periodic and chaotic phases. The Froude pendulum
with cubical and linear damping is a paradigm for such a system. In this work the driven Froude pendulum is studied by the
harmonic balancing method; the resulting nonlinear response curves are studied further for resonance and stability of symmetric
oscillations with relatively low damping. The stability analysis is carried out by transforming the system of equations to
the linear Mathieu equation. 相似文献
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Holger R. Dullin 《Zeitschrift für Physik B Condensed Matter》1994,93(4):521-528
Melnikov's method is applied to the planar double pendulum proving it to be a chaotic system. The parameter space of the double pendulum is discussed, and the integrable cases are identified. In the neighborhood of the integrable case of two uncoupled pendulums Melnikov's integral is evaluated using residue calculus. In the two limiting cases of one pendulum becoming a rotator or an oscillator, the parameter dependence of chaos, i.e. the width of the separatrix layer is analytically discussed. The results are compared with numerically computed Poincaré surfaces of section, and good agreement is found. 相似文献
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An experimental study of periodic and chaotic type aperiodic motions of a parametrically harmonically excited pendulum is presented. It is shown that a characteristic route to chaos is the period-doubling cascade, which for the parametrically excited pendulum occurs with increasing driving amplitude and decreasing damping force, respectively. The coexistence of different periodic solutions as well as periodic and chaotic solutions is demonstrated and various transitions between them are studied. The pendulum is found to exhibit a transient chaotic behaviour in a wide range of driving force amplitudes. The transition from metastable chaos to sustained chaotic behaviour is investigated. 相似文献
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4 混沌运动的特征[4]“混沌”一词有多义 ,而且在不同时期都有人使用这词 .在我国古代 ,混沌 (或浑沌 )谓之“想象中世界生成以前的状态” ,曹植《七启》中曰 :“夫太极之初 ,浑沌未分” ,《辞源》上解释为 :“天地未开辟以前之元气状态” .还用“混沌”形容“浑然一体 ,不可分割”的状态 ,在《易乾凿度》上曰 :“太易者 ,未见气也 .太初者 ,气之始也 .太终者 ,形之似也 .太素者 ,质之始也 .气似质具而未相离 ,谓之混沌” .在《庄子》三十三篇中的内篇之七叫应帝王 ,此篇末尾写 :“南海之帝为倏 .北海之帝为忽 .中央之帝为浑沌 .”可见此处… 相似文献
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Instabilities in the main parametric resonance area of a mechanical system with a pendulum 总被引:1,自引:0,他引:1
Vibrations of an autoparametric system, composed of a nonlinear mechanical oscillator with an attached damped pendulum, around the principal resonance region, are investigated in this paper. Approximate analytical solutions of the model are determined on the basis of the Harmonic Balance Method (HBM). Correctness of the analytical results is verified by numerical simulations and experimental tests performed on an especially prepared experimental rig. The influence of all essential parameters such as damping, excitation amplitude and frequency, nonlinear stiffness of the spring, on the localisation of the instability region and the system dynamics is presented in the work. Regions of regular system oscillations, chaotic motions, and full rotation of the pendulum are confirmed experimentally. 相似文献
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量子参数激励单摆的局域效应研究 总被引:1,自引:1,他引:0
分析了二能级原子在振幅调制主波场中动量扩散模型。这是一个量子参数激励单摆系统。这个量子系统在经典极限下表现混沌行为。在相同参数条件下,这个系统具有动力学特征。 相似文献