# 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
and*replication**regulation* - we discussted one-dimensional discrete time maps in general and their analysis
- and how to compute fixpoints and their stability
- we discussed
, the graphical analysis of these maps*cobwebbing* - we also discussed
and*period doubling* - 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
by Bob May.*Simple mathematical models with complicated dynamics*