In Spring 2010, this module will be taught by
who should be contacted for further information about this module.
| Day | Time | Room |
|---|---|---|
| Monday | 9-10 | LTA |
| Monday | 14-15 | LTA |
| Friday | 10-11 | LTA |
There will two assessed take-home assignments during the semester:
| Assessment component | Weighting | Date due |
|---|---|---|
| Class Test | 10% | Monday, 22nd. March 2010 [Week 7] |
| Coursework | 15% | Friday, 14th. May 2010 [Week 10] |
| Exam | 75% | May 2009 |
Exercise sheets will be posted on this webpage. Exercises may be handed in to me for feedback. In this case, they should be handed in to me within one week of the date that they are given out.
| Exercise Sheet | Solutions |
|---|---|
| Exercise Sheet 1 | Solutions Sheet 1 |
| Exercise Sheet 2 | Solutions Sheet 2 |
| Exercise Sheet 3 | Solution Sheet 3 |
| Exercise Sheet 4 | Solution Sheet 4 |
| Exercise Sheet 5 | Solution Sheet 5 |
Matlab code for Exercise sheet 5, question 2 can be found here.
Past examination papers for MS304 can be found by following the link in the left-hand menu. The 2006 past paper solutions can be found here.
Last years class test can be found here. A mock paper can be found here, with solutions here.
Current version of the Chaos and Fractals notes can be found here . These notes will be updated regularly.
A really good website explaining the dynamics of the Taffy machine can be found here.
Recently, Prof. Jim Al-Khalili (from the University of Surrey's Physics dept.) produced a documentary on Nonlinear Dynamics and Chaos which I thought was rather good!
| The Secret Life of Chaos | |
|---|---|
| Part 1 | Part 2 |
| Part 3 | Part 4 |
| Part 5 | Part 6 |
Matlab programs can be found below. To run them, load up Matlab and save the *.m files in the working directory. Then type the following at the matlab command line.
| Figures | Matlab codes |
|---|---|
| Figure 3: Chaotic Rabbits | figure3.m |
| Figure 7: Sensitive dependence on Initial conditions | figure7.m |
| Figure 8: Periodic orbit of Logistic map | figure8.m |
| Figure 16: Brusselator | figure16.m and brusselator.m |
| Figure 19: Transient chaos | figure19.m and lorenz.m |
| Figure 20: Rossler system | figure20.m and rossler.m |
| Figure 22: Poincare map of Rossler system | figure22.m, rossler_events_poincare.m and rossler.m |
| Figure 23: Rossler system 1D map | figure23.m, rossler_events_lorenz.m and rossler.m |
| Figure 27: Logistic map bifurcation diagram | figure27.m, Logistic-diagram.m |
| Figure 29: Cobweb Itermittency | figure29.m |
| Figure 30: Lyapunov exponent Logistic map | figure30.m |
| Figure 31: Bifurcation diagrams - Rossler system and Sine map | figure31a.m, figure31b.m, Rossler-diagram.m, Sine-diagram.m |
| Figure 32: Koch snowflake | figure32.m and kochstep.m |
| Figure 33: Message masking | figure33.m and mask-lorenz.m |
| Figures 12, 17 and 18: Phase plane | pplane7.m |
| Cobweb | cobweb.m |
| dfield7 | dfield7.m |
Matlab also has a really cool "inbuilt" movie of the Lorenz attractor. Just type at the matab command line "lorenz".
| Websites | |
|---|---|
| Dynamical Systems Web | Society for Industrial and Applied Mathematics Website |
| Scholarpedia | Scholarpedia website on dynamical systems |
| Tutorial website | Nonlinear Dynamics and Chaos intro website |
| Maths dept. research | The Maths dept. is one of the largest for Nonlinear Dynamics research |
| Evolution and Resilience | Research into evolution and resilience ofsocial systems using Maths |