A simple circuit realization of the tent map

TL;DR

This paper introduces a straightforward electronic circuit implementation of the tent map, demonstrating complex dynamical behaviors such as chaos and intermittency that closely align with theoretical predictions.

Contribution

A novel, simple circuit design for the tent map that accurately reproduces its complex dynamical phenomena using only passive components and integrated circuits.

Findings

Circuit exhibits fixed points, periodicity, chaos, and intermittency.

Experimental results closely match numerical simulations.

Implementation is simple and effective for studying dynamical systems.

Abstract

We present a very simple electronic implementation of the tent map, one of the best-known discrete dynamical systems. This is achieved by using integrated circuits and passive elements only. The experimental behavior of the tent map electronic circuit is compared with its numerical simulation counterpart. We find that the electronic circuit presents fixed points, periodicity, period doubling, chaos and intermittency that match with high accuracy the corresponding theoretical values