We study the existence and stability of periodic solutions of a canonical mass-spring model of electrostatically actuated Micro-Electro-Mechanical System (MEMS) by means of classical topological techniques like a priori bounds, Leray–Schauder degree and topological index. A saddle-node bifurcation is revealed, in analogy with the autonomous case. A quantitative estimation of the bifurcation value in terms of realistic values of the involved parameters can be made.
In the following paper, we present a nonlinear model of an atomic force microscope considering the potential of Lennard–Jones and the nonlinear friction produced by the squeeze film damping effect, between the cantilever and the sample. Specifically, we study the existence and stability of periodic solutions using the lower and upper solution method in the system without friction. The condition for persistence of the homocline orbit was established by Melnikov method when the model has nonlinear friction. In this sense, the analytic and numerical approach is presented to verify the solutions of the model.
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