S. I. Fadeev, “Nonlinear oscillations in the clock frequency generator excited by a sequence of concentrated electrostatic pulses coordinated with the oscillations ”, Sib. Zh. Ind. Mat., 2020, Volume 23, Number 3,Pages <nobr>123

Nonlinear oscillations in the clock frequency generator excited by a sequence of concentrated electrostatic pulses coordinated with the oscillations

S. I. Fadeev^ab

^a Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
^b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia

Abstract: Under consideration is the mathematical model of a clock frequency generator in which some high-frequency oscillations of a movable electrode are excited by a sequence of concentrated electrostatic pulses; wherein the times of pulse action are coordinated with the oscillations of the movable electrode by analogy with the well-known theory of a trigger clock. The results of studying the mathematical model provide a fairly complete understanding of the properties of the oscillations that are excited in the generator.

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

UDC: 519.62:621.38

Received: 26.12.2019
Revised: 26.12.2019
Accepted: 09.04.2020

DOI: 10.33048/SIBJIM.2020.23.310