论文标题
具有二分法噪声的参数谐波振荡器的稳定性
Stability of a parametric harmonic oscillator with dichotomic noise
论文作者
论文摘要
谐波振荡器是一个强大的模型，在检查非线性系统时可以作为限制情况出现。一个众所周知的事实是，在不驾驶的情况下，摩擦项的包含使相位空间的起源（这是系统的固定点）线性稳定。在这项工作中，我们将电报过程包括在振荡器频率的扰动中，例如描述粒子在外部磁场中带动电荷回旋的运动。这种有色噪声的强度增加能够改变固定点的质量。为了表征系统的稳定性，我们使用稳定度量，描述了系统相位空间位置的位移的生长并以封闭形式表达。我们将各自的指数扩展到光摩擦和低噪声强度，并比较确切的分析解决方案以及扩展到数值。我们的发现允许对几种物理系统进行稳定预测。
The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a fixpoint of the system -- linearly stable. In this work we include a telegraph process as perturbation of the oscillator's frequency, for example to describe the motion of a particle with fluctuating charge gyrating in an external magnetic field. Increasing intensity of this colored noise is capable of changing the quality of the fixed point. To characterize the stability of the system, we use a stability measure, that describes the growth of the displacement of the system's phase space position and express it in a closed form. We expand the respective exponent for light friction and low noise intensity and compare both, the exact analytic solution and the expansion to numerical values. Our findings allow stability predictions for several physical systems.
