Chaos & Complex Systems

Partial Bibliography

This list isn't comprehensive. But is should provide a useful starting place for many topics. See also the list of references at http://hornacek.coa.edu/dave/CSSS/

Economics and "Econophysics"

• Giovani L. Vasconcelos, A Guided Walk Down Wall Street: an Introduction to Econophysics. http://arXiv.org/abs/cond-mat/0408143.

  This article contains the lecture notes for the short course ``Introduction to Econophysics,'' delivered at the II Brazilian School on Statistical Mechanics, held in Sao Carlos, Brazil, in February 2004. The main goal of the present notes is twofold: i) to provide a brief introduction to the problem of pricing financial derivatives in continuous time; and ii) to review some of the related problems to which physicists have made relevant contributions in recent years.

Networks and Graphs

• T.S.Evans, Complex Networks. http://xxx.lanl.gov/abs/cond-mat/0405123.

  An outline of recent work on complex networks is given from the point of view of a physicist. Motivation, achievements and goals are discussed with some of the typical applications from a wide range of academic fields. An introduction to the relevant literature and useful resources is also given.

• Carlos Gershenson, Introduction to Random Boolean Networks. http://homepages.vub.ac.be/~cgershen/rbn/ and http://arXiv.org/abs/nlin/0408006.

  The goal of this tutorial is to promote interest in the study of random Boolean networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study their generic properties. Like this, RBNs have been used for exploring the configurations where life could emerge. The fact that RBNs are a generalization of cellular automata makes their research a very important topic. The tutorial, intended for a broad audience, presents the state of the art in RBNs, spanning over several lines of research carried out by different groups. We focus on research done within artificial life, as we cannot exhaust the abundant research done over the decades related to RBNs.

• M. E. J. Newman and Juyong Park, Why social networks are different from other types of networks. http://arXiv.org/abs/cond-mat/0305612.

  We argue that social networks differ from most other types of networks, including technological and biological networks, in two important ways. First, they have non-trivial clustering or network transitivity, and second, they show positive correlations, also called assortative mixing, between the degrees of adjacent vertices. Social networks are often divided into groups or communities, and it has recently been suggested that this division could account for the observed clustering. We demonstrate that group structure in networks can also account for degree correlations. We show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real-world networks.

• Bo Hu, et al. A Model of Weighted Network: the Student Relationships in a Class, http://arXiv.org/abs/cond-mat/0408125.

  A simple model is proposed to simulate the evolution of interpersonal relationships in a class. The small social network is simply assumed as an undirected and weighted graph, in which students are represented by vertices, and the extent of favor or disfavor between two of them are denoted by the weight of corresponding edge. Various weight distributions have been found by choosing different initial configurations. Analysis and experimental results reveal that the effect of first impressions has a crucial influence on the final weight distribution. The system also exhibits a phase transition in the final hostility (negative weights) proportion depending on the initial amity (positive weights) proportion.

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