# Introduction to Complex Systems

Prof. Dirk Brockmann, Winter Term 2021

# Lecture 3: One Dimensional Dynamical Systems

## Summary

• we discussed one dimensional dynamical systems like [ \dot x = f(x) ]
• we discussed the assumptions that are implicitly made for systems that can be modeled by ODEs like the above
• we covered the fixpoints analysis for the systems and conditions for stability of fixpoints
• we discussed how to find fixpoints by drawing $f(x)$ vs. $x$ (graphic analysis)
• we explained how to derive systems like the above for a few systems e.g.
• the two particle annihilation process
• an extended system that also involves reproduction
• an epidemic model

## Script

More information is provided in the script bit on One-Dimensional Dynamical Systems that is now online.

Read it, there's interactive stuff in it.

## Class Notes

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

## Further Information

• Again, I recommend the excellent book on dynamical systems by Steve Strogatz Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.
• Another good read is Mathematical Biology - An Introduction by James Murray