Nonlinear Oscillations in the Clock Frequency Generator Excited by a Sequence of Concentrated Electrostatic Pulses Coordinated with the Oscillations

S. I. Fadeev

doi:10.1134/S1990478920030047

Nonlinear Oscillations in the Clock Frequency Generator Excited by a Sequence of Concentrated Electrostatic Pulses Coordinated with the Oscillations

S. I. Fadeev

Differential Equations Section

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Abstract

Under consideration is the mathematical model of a clock frequency generator in whichsome high-frequency oscillations of a movable electrode are excited by a sequence of concentratedelectrostatic pulses; wherein the times of pulse action are coordinated with the oscillations of themovable electrode by analogy with the well-known theory of a trigger clock. The results ofstudying the mathematical model provide a fairly complete understanding of the properties of theoscillations that are excited in the generator.

Original language	English
Pages (from-to)	443-455
Number of pages	13
Journal	Journal of Applied and Industrial Mathematics
Volume	14
Issue number	3
DOIs	https://doi.org/10.1134/S1990478920030047
Publication status	Published - 1 Aug 2020

Keywords

boundary value problem
continuation of a solution with respect to a parameter
frequency generator
limit cycle
mathematical model
periodic oscillations
phase plane
stability

OECD FOS+WOS

1.01 MATHEMATICS

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10.1134/S1990478920030047

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title = "Nonlinear Oscillations in the Clock Frequency Generator Excited by a Sequence of Concentrated Electrostatic Pulses Coordinated with the Oscillations",

abstract = "Under consideration is the mathematical model of a clock frequency generator in whichsome high-frequency oscillations of a movable electrode are excited by a sequence of concentratedelectrostatic pulses; wherein the times of pulse action are coordinated with the oscillations of themovable electrode by analogy with the well-known theory of a trigger clock. The results ofstudying the mathematical model provide a fairly complete understanding of the properties of theoscillations that are excited in the generator.",

keywords = "boundary value problem, continuation of a solution with respect to a parameter, frequency generator, limit cycle, mathematical model, periodic oscillations, phase plane, stability",

author = "Fadeev, {S. I.}",

note = "Funding Information: The author was supported by the State Task to the Sobolev Institute of Mathematics (project no. 0314–2019–0013) and by the Complex Program of Basic Research of the Siberian Branch of the Russian Academy of Sciences “Interdisciplinary Integration Studies,” 2018–2020 (project no. 273). ACKNOWLEDGMENTS Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

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doi = "10.1134/S1990478920030047",

language = "English",

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N2 - Under consideration is the mathematical model of a clock frequency generator in whichsome high-frequency oscillations of a movable electrode are excited by a sequence of concentratedelectrostatic pulses; wherein the times of pulse action are coordinated with the oscillations of themovable electrode by analogy with the well-known theory of a trigger clock. The results ofstudying the mathematical model provide a fairly complete understanding of the properties of theoscillations that are excited in the generator.

AB - Under consideration is the mathematical model of a clock frequency generator in whichsome high-frequency oscillations of a movable electrode are excited by a sequence of concentratedelectrostatic pulses; wherein the times of pulse action are coordinated with the oscillations of themovable electrode by analogy with the well-known theory of a trigger clock. The results ofstudying the mathematical model provide a fairly complete understanding of the properties of theoscillations that are excited in the generator.

KW - boundary value problem

KW - continuation of a solution with respect to a parameter

KW - frequency generator

KW - limit cycle

KW - mathematical model

KW - periodic oscillations

KW - phase plane

KW - stability

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JF - Journal of Applied and Industrial Mathematics

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ER -

Nonlinear Oscillations in the Clock Frequency Generator Excited by a Sequence of Concentrated Electrostatic Pulses Coordinated with the Oscillations

Abstract

Keywords

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