References and Software
References from lecture
Bak, P., Tang, C. and Wiesenfeld, K. (1987) Self-organized criticality: an explanation
of 1 / f noise. Physical Review Letters 59, 381–384. [online]
http://dx.doi.org/10.1103%2FPhysRevLett.59.381
Batty, M. (2006) Rank Clocks. Nature 444, 592-596.
Brakman, S., Garretsen, J.H., Marrewijk, J.G.M. van, and Berg, M. van den (1999)
The return of Zipf: towards a further understanding of the rank-size distribution.
Journal of Regional Science 183-213.
Heppenstall, A.J., Evans, A.J. and Birkin, M.H., (2007) Genetic Algorithm
Optimisation of a Multi-Agent System for Simulating a Retail Market. Environment
and Planning B. v.34.
Heppenstall, A.J., Evans, A.J. and Birkin, M.H., (2006) Application of Multi-Agent
Systems to Modelling a Dynamic, Locally Interacting Retail Market. JASSS. vol 9(3).
Heppenstall, A.J., Evans, A.J. and Birkin, M.H. (2005), A Hybrid Multi-Agent/Spatial
Interaction Model System for Petrol Price Setting. Transactions in GIS 9(1): 35 - 51.
Heppenstall, A.J. and Ross, A.N. (2007) An Application of Agent-Based Modelling for
Investigating the Emergence of Structure and Dynamic Processes within a Complex
Retail Market. European Academy of Management Paris, May 16 - 19.
http://www.euram2007.org/
Heppenstall, A.J., McFarland, O.E. and Evans, A.E. (2005), The Application of MultiAgent Systems and Social Network Theory to Petrol Pricing on UK Motorways.
Lecture Notes in Artificial Intelligence 3690, pp. 551–554.
Nair, A.S., Jyh-Charn Liu, Rilett, L., and Gupta, S. (2001) Non-linear analysis of
traffic flow. Intelligent Transportation Systems, 2001. Proceedings. 2001 IEEE. 681685 [online] http://rtds.cs.tamu.edu/publications/conferences/CHAOS1.PDF
Scheffer, M., Bascompte, J., Brock, W.A., Brovkin, V., Carpenter, S.R., Dakos, V.,
Held, H., van Nes, E.H., Rietkerk, M. and Sugihara, G. (2009) Early-warning signals
for critical transitions. Nature 461, 53-59 [online]
http://www.nature.com/nature/journal/v461/n7260/full/nature08227.html
Shiner, J.S., Davison, Matt and Landsberg, P.T. (1999) On a simple measure for
complexity. Physical Review E, 59, (2), 1459-1464 [online]
http://dx.doi.org/doi:10.1103/PhysRevE.59.1459
Weaver, W. (1948) Science and Complexity. American Scientist. 36, 536-544.
[online] http://www.ceptualinstitute.com/genre/weaver/weaver-1947b.htm
Wilson, A.G. (1981) Catastrophe Theory and Bifurcation: Applications to Urban and
Regional Systems. Crook Helm Press. 0709927029
Zipf, G.K. (1949) Human Behavior and the Principle of Least Effort. Cambridge MA :
Addison-Wesley.
Materials used
The graph for 2009 populations is from Carnegie Mellon University PhD student
Brendan O’Connor’s blog:
http://anyall.org/blog/2009/05/zipfs-law-and-world-city-populations/
and is derived from populationdata.net figures:
http://www.populationdata.net/index2.php?option=palmares&rid=4&nom=grandesvilles
The logistic map figures are from the blog of Dan Olner, PhD student at Leeds:
http://www.coveredinbees.org/processing/exploringchaos/index.html
Further reading
A good starting point on complexity statistics is Bruce Edmunds’ Complexity
Bibliography:
http://bruce.edmonds.name/combib/
A good starting point on Kolmogorov complexity is Marcus Hutter’s site:
http://www.hutter1.net/ait.htm
If you are interested in the arguments around these issues, a good starting point is
the lectures by Seth Bullock and others from the Southampton Spring School in
Complexity Science, 2006:
http://videolectures.net/sscs06_southampton/
For a paper on analysis of a model of traffic flow, see:
Saavedra, P. and Velasco, R. M. (2009) Phase-space analysis for hydrodynamic
traffic models Physical Review E, 79, 066103 [online]
http://pre.aps.org/pdf/PRE/v79/i6/e066103
Good texts
The classic lay introduction to chaos is:
Gleick, J. (1987) Chaos: Making a New Science. http://www.around.com/chaos.html
Classical engineering treatment of chaos:
Tel, T. and Gruiz, M. Chaotic Dynamics. Cambridge University Press.
Programmers who want to build their own analysis software might want:
Steeb, W-H. (2002) The Nonlinear Workbook. World Scientific
Although we haven’t covered fractals here, they are an essential part of chaoscentred literature. If you want a good introductory text, then you could do worse than:
Hastings, H.M. and Sugihara, G. (1993) Fractals: A User’s Guide for the Natural
Sciences. Oxford Science Publications.
Software
Most developments in chaotic systems concentrate on purely mathematical systems
– they’re just very much easier to understand and deal with. So, most software does
the same. The following two sites include a wide variety of software, the latter site
including a lot of pure-maths treatments, however, there are some useful bits and
pieces, especially on the recurrence plots site.
Recurrence plots and other complexity measures:
http://www.recurrence-plot.tk/programmes.php
Complex Systems:
http://www.calresco.org/sos/software.htm