共查询到17条相似文献,搜索用时 109 毫秒
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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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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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《物理与工程》2019,(6)
以相图和庞加莱点作为表征手段,本文对受外力驱动的一种非线性动力学系统混沌摆的摆动行为进行研究,考察了该混沌摆系统的运动状态随驱动力频率变化的特征。同时我们建立了该系统的理论模型,通过数值计算模拟该混沌摆运动状态来验证实验结果。实验和仿真结果均表明,随着驱动力频率的增加,混沌摆会有周期和混沌运动状态交替出现的情况,且这种变化近乎为突变的。同时,也从数值仿真结果中观察到了混沌摆运动状态对驱动力频率这一参数的敏感性。本文阐述的仿真和测量研究可以作为本科生的大学物理实验课程中混沌摆实验项目的拓展内容,使有兴趣和能力的同学对非线性动力学系统的混沌现象有更深入的理解和认识。 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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对受迫非线性单摆系统进入混沌的道路进行了研究,发现单摆系统的运动是极其复杂的.目前在其他系统发现的进入混沌的通道,在该系统中几乎均可找到.这是一个介绍混沌运动的典型系统. 相似文献
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In this paper, the chaotic dynamics of a three-dimensional fractional-order chaotic system is investigated. The lowest order for exhibiting chaos in the fractional-order system is obtained. Adaptive schemes are proposed for control and synchronization of the fractional-order chaotic system based on the stability theory of fractional-order dynamic systems. The presented schemes, which contain only a single-state variable, are simple and flexible. Numerical simulations are used to demonstrate the feasibility of the presented methods. 相似文献
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掺杂超晶格是对同一材料交替掺入n-型和p-型杂质,形成n-i-p-i-n-i-p-i…一维阵列的周期结构。由于交替掺杂,衬底材料的导带受到周期调制形成一个个十分类似于正弦平方形式的量子阱。引入正弦平方势,在经典力学框架内,把粒子的运动方程化为具有阻尼项和受迫项的广义摆方程。用Jacobian椭圆函数和第一类全椭圆积分找到了无扰动系统的解和粒子振动周期,利用Melnikov方法分析了系统的全局分叉与Smale马蹄变换意义上的混沌行为,给出了系统通过级联分叉进入混沌的临界值。结果表明,对于异宿轨道,当参数满足条件 <πsech 时,系统出现了Smale马蹄变换意义上的混沌振荡。对于振荡型周期轨道,当参数满足条件 <πsech 时,产生了奇阶振荡型次谐分叉。注意到系统进入混沌的临界条件与它的参数有关,只需适当调节这些参数就可以避免或控制混沌,为光学双稳态器件的设计提供了理论分析。 相似文献
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The measurement of very small light forces has wide applications in many fields of physics. A common measurement method for small force detection is the determination of changes in the dynamic behavior of mechanical oscillators, either in amplitude or in frequency. The detection of slowly varying forces mostly requires long period oscillators, such as a torsion pendulum. We demonstrate the application of a macroscopic, low-noise, torsion balance oscillator for the detection of radiation pressure forces at the femto-Newton level. The system is "precooled" (removing excess seimic noise) to be only thermal noise limited. The demonstrated force sensitivity reaches the thermal limit. 相似文献
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We demonstrate experimental control of long-period orbits and arbitrary chaotic trajectories using a new chaos control technique called dynamic limiting. Based on limiter control, dynamic limiting uses a predetermined sequence of limiter levels applied to the chaotic system to stabilize natural states of the system. The limiter sequence is clocked by the natural return time of the chaotic system such that the oscillator sees a new limiter level for each peak return. We demonstrate control of period-8 and period-34 unstable periodic orbits in a low-frequency circuit and provide evidence that the control perturbations are minimal. We also demonstrate control of an arbitrary waveform by replaying a sequence captured from the uncontrolled oscillator, achieving a form of delayed self-synchronization. Finally, we discuss the use of dynamic limiting for high-frequency chaos communications. (c) 2002 American Institute of Physics. 相似文献