In network science, one can study the dynamics of a network — nodes being added or removed, edges being rewired — or the dynamics on the network — spins flipping from up to down in an Ising model, traffic flow along subway routes, an infection spreading through a susceptible population, etc. These have often been studied separately, on the rationale that they occur at different timescales. For example, the traffic load on the different lines of the Boston subway network changes on an hourly basis, but the plans to extend the Green Line into Medford have been deliberated since World War II.
In the past few years, increasing attention has been focused on adaptive networks, in which the dynamics of and the dynamics on can occur at comparable timescales and feed back on one another. Useful references:
- G. Demirel, F. Vazquez, G. A. Böhme and T. Gross (2012), “Moment-Closure Approximations for Discrete Adaptive Networks” [arXiv:1211.0449].
- K. Fehl et al. (2011). “Co-evolution of behaviour and social network structure promotes human cooperation” Ecology Letters 14: 546–51. PubMed:21463459.
- O. Gräser et al. (2011). “Analytic approach to co-evolving dynamics in complex networks: dissatisfied adaptive snowdrift game” New Journal of Physics 13, 8: 083015.
- T. Gross and B. Blasius (2008). “Adaptive coevolutionary networks: A review”. J R Soc Interface 5, 20: 259–71. PubMed:2405905.
- T. Gross and H. Sayama, eds (2009). Adaptive Networks: Theory, Models and Applications. Springer.
- C. Kamp (2010). “Untangling the interplay between epidemic spread and transmission network dynamics” PLoS Computational Biology 6, 11: e1000984. PubMed:2987842.
- M. Perc and A. Szolnoki (2009). “Coevolutionary games — a mini review”. BioSystems 99: 109–25. arXiv:0910.0826.
- H. Sayama et al. (2013). “Modeling complex systems with adaptive networks” Computers and Mathematics with Applications arXiv:1301.2561.
- L. B. Shaw and I. B. Schwartz (2010). “Enhanced vaccine control of epidemics in adaptive networks” Physical Review E 81, 4: 046120. PubMed:2931598.
- B. C. Stacey, A. Gros and Y. Bar-Yam (2011). “Beyond the Mean Field in Host-Pathogen Spatial Ecology”. arXiv:1110.3845.
- S. Van Segbroeck, F. C. Santos, and J. M. Pacheco (2010). “Adaptive contact networks change effective disease infectiousness and dynamics” PLoS Computational Biology 6, 8: e1000895. PubMed:2924249.
- S. Wieland et al. (2012), “Detecting and Describing Dynamic Equilibria in Adaptive Networks” European Physical Journal 212, 1: 99–113. arXiv:1210.1356.
- B. Wu et al. (2010). “Evolution of cooperation on stochastic dynamical networks” PLoS ONE 5, 6: e11187. PubMed:2894855.
(Disclaimer: I’ve met Thilo Gross and worked with Hiroki Sayama, but I don’t have any financial stake in the success of the anthology they co-edited.)
Originally posted as a comment at John Baez’s place. Reposted here because I’m like that about bibliographies. Last updated 27 November 2012.