Numerical Study of Nonlinear Oscillations in a Clock Frequency MEMS-Generator

S. I. Fadeev

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Under consideration is some mathematical model of a clock frequency generator, a deviceof the MEMS class (microelectromechanical systems). We numerically study the solution of thecorresponding second-order ordinary differential equation with nonlinear right-hand side and showthat there is a region of the model parameters in which the bounded solutions tend to a stablelimit cycle in the phase plane and, therefore, the periodic oscillations are stable with respectto the external perturbations. To determine the boundary of the region, we use the parametercontinuation method of the solution of the boundary value problem defining the limit cycle. Themodel leads to the numerical identification of the region of generator operability.

Original languageEnglish
Pages (from-to)296-307
Number of pages12
JournalJournal of Applied and Industrial Mathematics
Issue number2
Publication statusPublished - 1 May 2020


  • boundary value problem
  • frequency generator
  • limit cycle
  • mathematical model
  • parameter continuation method
  • periodic oscillations
  • phase plane
  • stability

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