This article is cited in 1 paper

Numerical study of nonlinear oscillations in a clock frequency MEMS-generator

S. I. Fadeev<sup>ab

a</sup> Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
^b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia

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.

Keywords: mathematical model, frequency generator, periodic oscillations, limit cycle, stability, phase plane, boundary value problem, parameter continuation method. .

UDC: 519.62:621.38

Received: 29.08.2019
Revised: 29.11.2019
Accepted: 05.12.2019

DOI: 10.33048/SIBJIM.2020.23.210

 English version: Journal of Applied and Industrial Mathematics, 2020, 14:2, 296–307

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