Binary-state dynamics on complex networks: pair approximation and beyond
REMARK: Notice special date and time
Speaker: Prof. James Gleeson
Affiliation: Department of Mathematics and Statistics, University of Limerick, IRELAND
Time: 3.00 PM
Date: Tuesday January 29th 2013
Location: Merrion Seminar Room, Ground Floor, NexusUCD, Blocks 9 & 10, Belfield Office Park
Abstract:
A wide class of binary-state dynamics on complex networks---including, for example, the voter model, the Bass diffusion model, and threshold models---can be described in terms of transition rates (spin-flip probabilities) that depend on the number of nearest neighbours in each of the two possible states. High-accuracy approximations for the emergent dynamics of such models on uncorrelated, infinite networks are given by recently-developed compartmental models or approximate master equations (AME). Pair approximations (PA) and mean-field theories can be systematically derived from the AME; we show that PA and AME solutions can coincide in certain circumstances. This facilitates bifurcation analysis, yielding explicit expressions for the critical (ferromagnetic/paramagnetic transition) point of such dynamics, closely analogous to the critical temperature of the Ising spin model.
Series: Applied and Computational Mathematics Seminar
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