具有二分噪声的参量谐振子的稳定性
Stability of a parametric harmonic oscillator with dichotomic noise
摘要：
谐振子是一个强大的模型，可以作为一个极限情况下，检查一个非线性系统。一个众所周知的事实是，在没有驱动的情况下，包含摩擦项使得相空间的原点-这是系统的不动点-线性稳定。在这项工作中，我们包括一个电报过程作为扰动的振荡器的频率，例如，描述的运动与波动的电荷在外部磁场旋转的粒子。增加这种有色噪声的强度能够改变固定点的质量。为了表征系统的稳定性，我们使用了一个稳定性测度，它描述了系统相空间位置的位移的增长，并以封闭形式表示。我们扩大各自的指数为轻摩擦和低噪声强度和比较，精确的解析解和扩展到数值。我们的研究结果允许几个物理系统的稳定性预测。
英文摘要：
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.
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