Finite differences for design of nonlinear discrete time oscillators

  • Authors: Zaitsev V.1, Fedyunin E.2, Shilin A.1
  • Affiliations:
    1. Самарский национальный исследовательский университет им. акад. С.П. Королева
    2. АО «Ракетно-космический центр «Прогресс»
  • Issue: Vol 20, No 2 (2017)
  • Pages: 35-41
  • Section: Articles
  • URL: https://journals.ssau.ru/pwp/article/view/7095
  • ID: 7095

Cite item

Full Text

Abstract

The method of finite differences is used for sampling of time in mathematical models - the differential motion equations of self-oscillatory systems of Thomson type. It is shown that both the right, and left differences allow to keep conservatism of a linear oscillatory contour of self-oscillatory system, but the iterated differential motion equations (discrete mappings) give only the left differences. The method of slow-changing amplitudes is applied to approximate analysis of the finite differences equations. Violations in dynamics of a phase of self-oscillations upon transition to discrete time are noted. The mode of generation of chaotic self-oscillations at high levels of excitement of the discrete oscillator of Van der Pol is shown. New approach to design of self-oscillatory systems with discrete time is offered. Parameters of the difference operators are selected from it taking into account invariance of the shortened equations for slow complex amplitudes of rather temporal sampling.

About the authors

V.V. Zaitsev

Самарский национальный исследовательский университет им. акад. С.П. Королева

Author for correspondence.
Email: zaitsev@samsu.ru

E.Yu. Fedyunin

АО «Ракетно-космический центр «Прогресс»

Email: fedyunin_eduard@mail.ru

A.N. Shilin

Самарский национальный исследовательский университет им. акад. С.П. Королева

Email: shilax@yandex.ru

References

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2017 Zaitsev V., Fedyunin E., Shilin A.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

СМИ зарегистрировано Федеральной службой по надзору в сфере связи, информационных технологий и массовых коммуникаций (Роскомнадзор).
Регистрационный номер и дата принятия решения о регистрации СМИ: серия ФС 77 - 68199 от 27.12.2016.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies