Introduction to Chaos in Deterministic Systems

TL;DR

This paper provides an accessible introduction to chaos theory, illustrating key properties of chaotic systems like the logistic map and bifurcation diagrams, aimed at beginners with basic algebra knowledge.

Contribution

It offers a simple, non-technical overview of chaos concepts, highlighting important properties and universal behaviors, with references for further mathematical study.

Findings

Illustration of chaos properties using logistic map

Explanation of bifurcation diagrams and universality

Accessible introduction suitable for beginners

Abstract

The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using the logistic map and its bifurcation diagram. We also show the universality found in "the route to chaos". The user is only required to have notions of algebra, so it is quite accessible. The formal basis of chaos theory are not covered in this introduction, but are pointed out for the reader interested in them. Therefore, this package is also useful for people who are interested in going deep into the mathematical theories, because it is a simple introduction of the terminology, and because it points out which are the original sources of information (so there is no danger in falling in the trap of "Learn Chaos in 48 hours" or "Bifurcation Diagrams for Dummies"). The included exercises are suggested for consolidating the covered topics. The on-line resources are highly recommended for extending this brief induction.