Logo: University of Surrey
Logo: Department of Mathematics

MAT3007: Nonlinear Dynamics and Chaos

Lecturer

In Spring 2010, this module will be taught by

Dr David Lloyd

who should be contacted for further information about this module.

Class Details

Day Time Room
Monday 9-10 LTA
Monday 14-15LTA
Friday 10-11LTA

Assessment

There will two assessed take-home assignments during the semester:

Assessment componentWeightingDate due
Class Test10%Monday, 22nd. March 2010 [Week 7]
Coursework15%Friday, 14th. May 2010 [Week 10]
Exam75%May 2009

Unassessed Assignments

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.

Selected Texts

Past Examination Papers

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.

Notes

Current version of the Chaos and Fractals notes can be found here . These notes will be updated regularly.

Movies

Movies
Chaotic Double Pendulum Chaotic Water wheel
Wing flutter: A Hopf Bifurcation Taffy machine: ``stretching and folding" chaos
Chemical Oscillations and Pattern formation Fractals
Secret communications with chaos

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 5Part 6

Computer Resources

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 planepplane7.m
Cobwebcobweb.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

I list below several interesting websites related to this course.
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. researchThe Maths dept. is one of the largest for Nonlinear Dynamics research
Evolution and ResilienceResearch into evolution and resilience ofsocial systems using Maths