A simple electronic device to experiment with the Hopf bifurcation

Authors

  • D. N. Rim Faculty of Exact and Natural Sciences National University of Cuyo
  • P. Cremades Faculty of Exact and Natural Sciences National University of Cuyo
  • Pablo Federico Kaluza Interdisciplinary Institute of Basic Sciences, National Scientific and Technical Research Council (CONICET) & Faculty of Exact and Natural Sciences, National University of Cuyo.

DOI:

https://doi.org/10.31349/RevMexFisE.65.58

Keywords:

Hopf bifurcation, dynamical systems, electronic circuit, repressilator

Abstract

We present a simple low-cost electronic circuit that is able to show two different dynamical regimens with oscillations of voltages and with constant values of them. This device is designed as a negative feedback three-node network inspired in the genetic repressilator. The circuit's behavior is modeled by a system of differential equations which is studied in several different ways by applying the dynamical system formalism, making numerical simulations and constructing and measuring it experimentally. We find that the most important characteristics of the Hopf bifurcation can be found and controlled. Particularly, a resistor value plays the role of the bifurcation parameter, which can be easily varied experimentally. As a result, this system can be employed to introduce many aspects of a research in a real physical system and it enables us to study one of the most important kinds of bifurcation.

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Published

2019-01-21

How to Cite

[1]
D. N. Rim, P. Cremades, and P. F. Kaluza, “A simple electronic device to experiment with the Hopf bifurcation”, Rev. Mex. Fis. E, vol. 65, no. 1 Jan-Jun, pp. 58–63, Jan. 2019.

Issue

Vol. 65 No. 1 Jan-Jun (2019): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2019 Pablo Federico Kaluza

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

Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.