I started studying Chaos Theory for two reasons. First of all I wanted to understand how the tools from Chaos Theory can be used to study complex systems – particularly time-series data. Secondly Chaos Theory has always had a mystical feel to it and I wanted to get a better understanding of the main concepts and how they relate to other fields of mathematics.
When I am just starting to learn about a new scientific field I like to read popular science books on the subject. If you are like this too, then the following books may be of interest to you:
- Sync: The Emerging Science of Spontaneous Order by Steven H. Strogatz. This is the book that got me interested in the subject to begin with. It is well written and leave you wanting more. Luckily the auther has also written a text-book on the subject, which I whole heartily recommend as well (see below).
- Chaos: Making a New Science by James Gleick. This book has a broader focus than Synch, and tells the story of how the study of chaotic systems became a science.
If any of the books above peaked your interest in the study of non-linear dynamics, the book below will give you a more thorough introduction to the field.
- Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering by Steven H. Strogatz. This book is amazing. The author states in foreword that the book is written in an informal language to make it captivating, without skimping on the mathematical rigour. In this he succeeds and it makes the book more interesting to read. It is also filled with examples which is perfect for someone who approaches the field as an applied science.
If reading an entire text-book seems like too much work, and you just want to get straight to the tools, then the following paper may be of interest. However, they are a bit denser and may be more difficult to follow if you do not have some of the background knowledge.
- Estimating the Fractal Dimension of Chaotic Time Series by J. Theiler. This paper is well written and serves as a good introduction to the tools that Chaos Theory brings to the table when analysing time-series data. It discusses the strength and weaknesses of the different approaches to characterizing the fractal dimension of a time-serie.
- Estimation of the Kolmogorov entropy from a chaotic signal by P. Grassberger and I. Procaccia. This paper introduces one of the methods for establishing the fractal dimension of a time-series. The approach is also shortly described in the paper mentioned above, but this paper goes into more detail.
There are, of course, online courses. I have not followed any of these yet, but I leave them here for future reference:
Finally, the subject was interesting enough that I decided to write a blog posts about. It can be read here.