A Simple Electronic Circuit Demonstrating Hopf Bifurcation for an Advanced Undergraduate Laboratory
Adaptation and Self-Organizing Systems
2023-01-05 v1
Abstract
A nonlinear electronic circuit comprising of three nodes with a feedback loop is analyzed. The system has two stable states, a uniform state and a sinusoidal oscillating state, and it transitions from one to another by means of a Hopf bifurcation. The stability of this system is analyzed with nonlinear equations derived from a repressilator-like transistor circuit. The apparatus is simple and inexpensive, and the experiment demonstrates aspects of nonlinear dynamical systems in an advanced undergraduate laboratory setting.
Keywords
Cite
@article{arxiv.2210.09616,
title = {A Simple Electronic Circuit Demonstrating Hopf Bifurcation for an Advanced Undergraduate Laboratory},
author = {Ishan Deo and Krishnacharya Khare},
journal= {arXiv preprint arXiv:2210.09616},
year = {2023}
}