Geodesic
The simulation of nonlinear oscillations in a micro clock generator
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 4, pp. 499-511.

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In this paper, we consider a mathematical model of a new type of a microgenerator, based on generating the oscillations of a mobile electrode in a micro-gap due to electrostatic forces. The principle of operation of the generator is analogous to the well-known theory of the clock-escapement mechanism, with the difference that in the equation of motion the form of the right-hand side corresponds to the electrostatic nature of the impulse action. The numerical analysis shows that the bounded oscillations with an increase in time tend towards a stable limit cycle in the phase plane and, thereby, the emerging oscillations are stable with respect to external perturbations. In studying periodic oscillations, depending on the parameters of a model, we use the solution of the boundary value problem for the equation with a discontinuous right-hand side, transformed to a form allowing the application of the numerical continuation method. In this way, the area in the plane of the model parameters is defined, in which stable limit cycles exist. 
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S. I. Fadeev; V. V. Kogai. The simulation of nonlinear oscillations in a micro clock generator. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 4, pp. 499-511. http://geodesic.mathdoc.fr/item/SJVM_2019_22_4_a7/

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