# A simple electronic device to experiment with the Hopf bifurcation

## TL;DR

This paper introduces a simple, low-cost electronic circuit that demonstrates the Hopf bifurcation, allowing for experimental study and control of dynamical behaviors in a physical system.

## Contribution

The authors design and analyze a novel electronic circuit inspired by the genetic repressilator to experimentally demonstrate and control the Hopf bifurcation.

## Key findings

- The circuit exhibits two distinct dynamical regimes with oscillations and steady states.
- The bifurcation parameter can be easily tuned via a resistor value.
- The system effectively models key features of the Hopf bifurcation.

## 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.