Lecture Courses
PX391 Nonlinearity, Chaos, Complexity
Lectures are second half of spring term- past papers and solutions to the (four) problem sheets are available from the Physics Undergraduate office. Problem sheet solutions are available here and in hard copy from the Undergraduate Office.
Handouts:
classification of fixed points
The Netlogo website, home to Netlogo free-to-download package for modelling complex systems
My (not so elegant or fast) Matlab routine for flocking birds (Vicsek model) .
There are some fun movie clips courtesy MIT, eg the coupled pendulum:
Takens theorem movies, see the supplimentary info of Sugihara et al (2012)
Forgotten the maths? Have a look on Khan Academy:
How to sketch curves: Derivative applications
What is a Taylor expansion
How to Solve quadratics by formula
Basic Trig Identities
Lecture notes- these are verbatim as given in the lectures- not textbook quality! Note I may not stick to this exact schedule.
Lecture 5+6 see also handout on classification of fixed points
MPAGS Module : Time Series Analysis- an Introduction to Advanced Methods
Given in Autumn Term.
Lecture Notes
These are written to supplement, not replace, the lectures, and so are terse in style.
lecturenotes-spectralestimates.pdf
lecturenotes-generalizingfourier.pdf
lecturenotes_structurefunctions.pdf
lecturenotes_complex_measures.pdf
Project and Assessment
To take part in this course for credit you will need to do the exercise in data analysis- this will be described in detail in the lectures. You will need to look at the RXTE websites:
The Readme files on RXTE Quicklook datafiles and the datasets are: RXTE ASM Lightcurves
For what is expected in the report: report.pdf
Reference material
Matlab's own demos (both in Matlab and in the signal processing and wavelets toolboxes) are highly recommended.
Basic Fourier theory: basicfourierintro.pdf (courtesy The Math Forum@Drexel Library) and Matlab intro basicfouriermatlab.pdf
Higher Order Spectra: ddw_review_hos_2003.pdf
Wavelets: torrence_compo_wavelets_1998.pdf farge_wavelets_turb1996.pdf farge_wavelets_turb2002.pdf
Observing power laws: clausetpowerlaws.pdf
Pi theorem, Buckingham's original paper: buckingham1914.pdf and an application to turbulence and SOC: chapmanpitheorem.pdf