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.
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 Mathematical Biology - An Introduction by James Murray