Written on 24.07.2023 11:11 by Dan Hill
First, I just want to note that the `Qualification Sheet' had a typo in it, which has now been corrected. I would recommend you attempting this sheet, as it uses lots of different topics that we covered during the course.
Secondly, here are some additional resources to help with revision:
- The textbook 'Introduction to Applied Nonlinear Dynamical Systems and Chaos' by Stephen Wiggins https://link.springer.com/book/10.1007/b97481 (should be available to download using Uni VPN or on campus) has lots of extra exercises that you can use to practise computing invariant manifolds, etc.
- If you are having trouble drawing phase diagrams and bifurcation diagrams, a useful website to help you is
- Phase Plane Plotter : Built with Processing and Processing.js (kevbase.com) - Plotting 2D phase portraits (including in polar coordinates)
- Bifurcation Diagram Plotter : Built with Processing and Processing.js (kevbase.com) - Plotting bifurcation diagrams
I would recommend trying to plot the diagram yourself first, and then comparing with the numerical plot.
If you have any questions during revision, you can send me an email and I will try to help as much as I can.
All the best,