Lecture 2: The logistic map

Summary

• we discussed the logistic map [ x_{n+1}=\lambda x_{n}(1-x_{n})\quad\text{with}\quad n=0,1,2,3... ]
• we motivated it using discrete time population growth and the combination of replication and regulation
• we discussted one-dimensional discrete time maps in general and their analysis
• and how to compute fixpoints and their stability
• we discussed cobwebbing, the graphical analysis of these maps
• we also discussed period doubling and
• the emergence of deterministic chaos

Script

More information is provided in the script bit The logistic map in the Script section.

Class Notes

The class notes from the online whiteboard are available, too.

Further Information

A lot more can be said about the logistic map, one-dimensional non-linear maps in general, deterministic chaos and so forth. If you want to dive deeper into the material I suggest the following:

• The book on dynamical systems Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering by Steven Strogatz, chapter 10.
• The seminal 1976 Nature paper Simple mathematical models with complicated dynamics by Bob May.