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.
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ACKNOWLEDGMENTS
The author is grateful to E. G. Kostsov due to whose initiative the research on the mathematical model of a generator was conducted, as well as to V. V. Kogai and V. K. Korolev for their participation in the work.
Funding
The author was supported by the State Task to the Sobolev Institute of Mathematics (project no. 0314–2019–0013).
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Translated by L.B. Vertgeim
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Fadeev, S.I. Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator. J. Appl. Ind. Math. 14, 296–307 (2020). https://doi.org/10.1134/S1990478920020088
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DOI: https://doi.org/10.1134/S1990478920020088