Complexity Explorer Santa Fe Institute

This course is no longer in session.

Introduction to Dynamical Systems and Chaos (Fall 2018)

Lead instructor:

9.7 Additional Resources (Optional) » Additional Resources

Reaction-diffusion Systems.  This is a fairly advanced topic.  I find that the math and chemistry can get pretty complex.

  • Edelstein-Keshet, Leah. Mathematical models in biology. Vol. 46. Siam, 1988.  This is a fantastic book.  It is an exceptionally clear and well-written introduction to a range of topics.  In addition to nice coverage of reaction-diffusion systems and pattern formation, it include finite difference equations (i.e., iterated function) and ordinary differential equations.  Highly recommended.

  • Britton, Nicholas F. Essential mathematical biology. Springer, 2003.  A clear introductory survey of a topics in mathematical biology.

  • Murray, James D. Mathematical Biology I: An Introduction, Springer.  2007.  A comprehensive treatment of mathematical biology at a fairly advanced level.  In my opinion less accessible than the above two references.

Belousov-Zhabotinsky Reactions.  

General Pattern Formation

The three books by Philip Ball are a fantatsic introduction to shapes and patterns in physical and natural systems.  Clear and interesting, with a minimum of mathematics.

  • Ball, Philip. Shapes: nature's patterns: a tapestry in three parts. Vol. 1. Oxford University Press, 2011.

  • Ball, Philip. Flow: nature's patterns: a tapestry in three parts. Vol. 2. Oxford University Press, 2011.

  • Ball, Philip. Branches: nature's patterns: a tapestry in three parts. Vol. 3. Oxford University Press, 2011.

Other books on pattern formation include:

  • Adam, John A. Mathematics in nature: Modeling patterns in the natural world. Princeton university press, 2006.  An engaging account of an eclectic set ot topics, including several examples of pattern formation.  Most of the book assumes a knowlege of calculus.