# 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