A canonical mass–spring model of electrostatically actuated Micro-Electro-Mechanical System (MEMS) is studied. We investigate the existence and bifurcations of the periodic solution by means of the continuation theorem of Mańasevich and Mawhin with techniques of a priori estimate and bifurcation theory. The main results answer the open problem proposed by P. Torres in the known literature. It also reveals that the system undergoes saddle node and period doubling bifurcation leading to the multiplicity of periodic solution. Moreover, bistability of periodic solution generated by the combination of these bifurcations is detected for the first time, which provides some new insight into the so called pull-in instability in the system. At last, periodic orbits with different stability and corresponding time series are given to illustrate the results.

研究了静电驱动微机电系统 (MEMS) 的标准质量-弹簧模型。我们通过 Mañasevich 和 Mawhin 的延拓定理以及先验估计和分岔理论的技术来研究周期解的存在和分岔。主要结果回答了 P. Torres 在已知文献中提出的开放问题。它还揭示了系统经历了鞍节点和倍周期分岔，导致了周期解的多重性。此外，首次检测到由这些分岔组合产生的周期解的双稳态，这为系统中所谓的拉入不稳定性提供了一些新的认识。最后给出了不同稳定性的周期轨道和对应的时间序列来说明结果。