In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.
在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。
The testing results show that the performance of the cross-coupled crystal oscillator meets the system demands.
测试结果表明，本文所设计的交叉耦合晶体振荡器满足系统的要求。
ABSTRACT The dynamical behaviors of coupled oscillator systems, such as phase-locking and death phenomena, have been studied for more than...
交联振荡器系统的相锁和停振等现象的研究已有十多年的历史。
ABSTRACT The dynamical behaviors of coupled oscillator systems, such as phase-locking and death phenomena, have been studied for more than ten years.
交联振荡器系统的相锁和停振等现象的研究已有十多年的历史。
In this thesis, the author systematically studies and develops the theory of coupled oscillator systems about the phenomena of phase-locking, death, internal entrainment, and obtains some new results. The author considers social economic system as a coupled large system, formed by its departments.
本文从交联振荡器系统理论出发，从数学上发展了已有的交联振荡器的单向交联、多重交联等理论，系统地研究了连通交联振荡器系统以及时滞交联振荡器系统的相锁、停振、内部传输等问题，得到了一批新结果。
In addition, there exists the high dimensional oscillator in physics, In its Hamiltonian coordinates and momenta are coupled. For instance, quantumHall system does so.
另外，物理问题中有一类型振子是高维的，在其哈密顿量中动量和坐标是相互耦合的，比如量子霍尔系统就是如此。
In Chapter 2, a LC tank based back-gate coupling current-reused complementary cross-coupled quadrature voltage control oscillator is presented.
第二章的内容主要在设计一个LC共振腔结合背闸极耦合之电流再利用式互补式交叉耦合对正交四相位压控振荡器。
This thesis presents a self-coupled voltage-controlled LC oscillator which originates from the concept of both the current coupling of quadrature LC oscillator and the self coupling of ring oscillator.
此控制频率变化的方法，乃是利用四相位LC振荡器的电流耦合以及环型振荡器的自耦合之观念延伸而来。
To improve the resolution of time to digital inverter, many ways are developed such as analogue time expansion, vernier difference technique, analogue time interpolation technique, array of coupled oscillator techniques, array delay locked loops, and time interpolation using passive RC delay lines. More accuracy time to digital converter can be developed along with the development of micro-electronics techniques.
为提高时间分辨率，人们想了很多方法，包括模拟扩展技术、游标技术、模拟内插技术、耦合振荡技术、延迟锁定阵列技术、RC延迟线内插技术等，并且随着微电子技术的不断发展，可以实现更高精度的时间测量。
Based on Lin's adiabatic approximation theory, the validity of the adiabatic approximation for coupled oscillator was discussed in this paper.
本文在Lin的绝热近似基础上讨论了耦合振子绝热近似的有效性。
Adiabatic Approximation Model for Coupled Oscillator
耦合振子绝热近似模型
This paper briefly presents the principle of FET oscillator with a Hi-Q dielectric resonator feedback, which is considered to be similar to that of a reflection oscillator with a Hi-Q dielectric resonator coupled to the gate of a FET.
本文扼要分析了高Q介质反馈型FET振荡器的原理，认为介质反馈型振荡器类同于高Q介质谐振器与FET栅极耦合的反射型振荡器。
By constructing a Lyapunov function, the sufficient conditions for global stability of the positive equilibrium are obtained. (2) Coupled oscillator systems with delayed feedback is considered, when angular frequency is a constant.
通过构造李雅普诺夫泛函，给出了模型正平衡点全局稳定性的充分条件。（2）在角频率相同的条件下，对一类时间延迟耦合振荡器模型进行了研究。
Evolution of Coordinate Second-Order Coupled System of a Harmonic Oscillator and an Anharmonic Oscillator with q ￣ 4
具有q~4的非谐振子与谐振子的坐标二阶耦合系统的演化
Multimode oscillations in an inductor coupled van der Pol oscillator system
电感耦合的vanderpol振荡器系统中的多模式振荡
For a coupled nonlinear oscillator system with diffusion and gradient couplings, spatial Fourier transformation is performed and the dynamic equations of various space modes are derived.
对于一类同时存在扩散耦合和梯度耦合的非线性振子系统，通过空间傅里叶变换，得到具有不同波矢的各运动模式的相互独立的运动方程。
In this paper, response prediction of the double-oscillator system under nonlinear coupled system is obtained by using the. Stochastic averaging method.
本文对统计能量法的基础理论进行了研究，应用随机平均法研究随机激励下带有非线性刚度耦合的系统，得到了系统的响应估算。
The design of a new quadrature VCO (Voltage Controlled Oscillator) is obtained through a cross-coupled double LC oscillator, using the coupling coefficient to control oscillation frequency.
通过对两个相同的LC振荡器进行交差耦合，用耦合系数来控制输出频率，设计了一种新型精准正交正弦波压控振荡器。
Utilizing the general linear quantum transformation theory, we give the exact expressions of evolutionary operator's matrix elements, wave function, expectation value of an observable and partition function, for multi-dimensional coupled and forced quantum oscillator.
运用广义线性量子变换的普遍理论求解多维耦合受迫量子谐振子，给出了系统演化算符的矩阵元、波函数、力学量期望值和配分函数的严格表达式。
Optimum Coupled Line Length of Band Reflection Type Cavity Stabilized Gunn Oscillator
频带反射型腔稳体效应振荡器的最佳耦合线长度