Abstract

Under consideration is some mathematical model of a clock frequency generator, a device of the MEMS class (microelectromechanical systems). We numerically study the solution of the corresponding second-order ordinary differential equation with nonlinear right-hand side and show that there is a region of the model parameters in which the bounded solutions tend to a stable limit cycle in the phase plane and, therefore, the periodic oscillations are stable with respect to the external perturbations. To determine the boundary of the region, we use the parameter continuation method of the solution of the boundary value problem defining the limit cycle. The model leads to the numerical identification of the region of generator operability.

中文翻译：

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时钟频率MEMS发生器中非线性振荡的数值研究

摘要

正在考虑时钟频率发生器的某种数学模型，该时钟频率发生器是MEMS类的设备（微机电系统）。我们通过数值研究对应的具有右手侧非线性项的二阶常微分方程的解，并显示出模型参数中存在一个区域，在该区域中，有界解趋向于在相平面中具有一个稳定的极限环，因此，周期性振荡相对于外部扰动是稳定的。为了确定区域的边界，我们使用定义极限环的边界值问题的解的参数延续方法。该模型导致发电机可操作性区域的数值识别。