Introduction to Complex Systems

Prof. Dirk Brockmann, Winter Term 2021

Lecture 2: The logistic map


  • 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


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: