## Abstract

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 language | English |
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Pages (from-to) | 296-307 |

Number of pages | 12 |

Journal | Journal of Applied and Industrial Mathematics |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 May 2020 |

## Keywords

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