Simulation of Nonlinear Oscillations in a Micro-Generator of Clock Frequency

S. I. Fadeev, V. V. Kogai

Research output: Contribution to journalArticlepeer-review


In this paper, we consider a mathematical model of a new-type micro- generator. The model is based on excitation by electrostatic forces of oscillations of a mobile electrode in a micro gap. The principle of operation of the micro-generator is similar to the well-known theory of clock with a striking escapement mechanism. The difference is that in the equation of motion, the form of the right-hand side takes into account the electrostatic nature of the pulsed action. The numerical analysis shows that with time the bounded oscillations in the phase plane tend to a stable limit cycle, and thus the emerging oscillations are stable towards external perturbations. Studying periodic oscillations in dependence on model parameters relies on the boundary value problem solution for an equation with a discontinuous right-hand side transformed so that to enable application of the method of solution continuation with respect to a parameter. In this way, the domain in the plane of model parameters in which stable limit cycles exist is defined.

Original languageEnglish
Pages (from-to)407-417
Number of pages11
JournalNumerical Analysis and Applications
Issue number4
Publication statusPublished - 1 Oct 2019


  • mathematical model
  • micro-generator
  • Cauchy problem
  • boundary value problem
  • periodic oscillations
  • limit cycle
  • phase plane
  • continuation of solution with respect to a parameter


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