# Lecture 3: One Dimensional Dynamical Systems

## Summary

- we discussed one dimensional dynamical systems like [ \dot x = f(x) ]
- we discussed the
that are implicitly made for systems that can be modeled by ODEs like the above*assumptions* - we covered the
for the systems and conditions for*fixpoints analysis*of fixpoints*stability* - 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*

- the two particle

## 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.

## Recording

## 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
by James Murray*Mathematical Biology - An Introduction*