Bifurcation transitions in dynamic systems of pulse voltage regulator


Cite item

Full Text

Abstract

In this article bifurcations in nonlinear dynamical systems are considered and special attention is paid to bifurcations-crises, which are identified with catastrophes in systems. The qualitative change in the phase portrait that occurs when the parameter m of the system changes is called the bifurcation of the phase portrait. The value of the system parameter m = m0, at which bifurcation occurs, is called the bifurcation value of the parameter (or bifurcation point). Mathematical models are presented in unsaturated mode; in saturation mode. Sufficient conditions are given under which the Andronov–Hopf bifurcation takes place. Quantitative relations are determined for the conditions under which the Andronov–Hopf bifurcation takes place in the system. Numerical values of parameters are entered, at which the system takes a quite compact, but quite informative form.

About the authors

Andrei A. Voronoi 

Povolzhskiy State University of Telecommunications and Informatics

Author for correspondence.
Email: arminvanburn@yandex.ru

Nikita A. Cilimbaev

Povolzhskiy State University of Telecommunications and Informatics

Email: artes3009@rambler.ru

Vladimir A. Ushmodin

Povolzhskiy State University of Telecommunications and Informatics

Email: ushmodin.13@gmail.com

References

  1. Antipov O.I., Neganov V.A. Analysis and Prediction of the Behavior of Time Series: Bifurcations, Disasters, Synergetics, Fractals and Neural Networks. Moscow: Radiotehnika, 2011, 350 p. (In Russ.)Belyh V.N. An elementary introduction to the qualitative theory and theory of bifurcations of dynamical systems. Sorosovskij obrazovatel’nyj zhurnal, 1997, no. 1, pp. 115–121. (In Russ.)Dmitrikov V.F., Shushpanov D.V. Stability and Electromagnetic Compatibility of Devices and Power Supply Systems. Moscow: Gorjachaja linija – Telekom, 2018, 540 p. (In Russ.)Dmitrikov V.F., Shushpanov D.V. The main scientific problems of building domestic aggregated (complex) devices and distributed power supply systems and the reasons for their characteristics lagging behind modern foreign analogs. Physics of Wave Processes and Radio Systems, 2018, vol. 21, no. 3, pp. 7–11. URL: https://journals.ssau.ru/index.php/pwp/article/view/7011. (In Russ.)

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2020 Voronoi  A., Cilimbaev N., Ushmodin V.

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