A Simple Electronic Circuit Demonstrating Hopf Bifurcation for an Advanced Undergraduate Laboratory

TL;DR

This paper presents a simple, inexpensive electronic circuit that demonstrates Hopf bifurcation, allowing advanced undergraduates to explore nonlinear dynamical systems through hands-on experiments.

Contribution

It introduces a novel, accessible circuit design that effectively illustrates Hopf bifurcation phenomena in an educational laboratory setting.

Findings

The circuit exhibits two stable states: a uniform and an oscillating state.

Transition between states occurs via Hopf bifurcation.

The system's stability is analyzed using nonlinear equations.

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.