Exploring the adaptive voter model dynamics with a mathematical triple jump

Holly A Silk, Güven Demirel, Martin E Homer, Thilo Gross

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 Citations (Scopus)
365 Downloads (Pure)

Abstract

Progress in theoretical physics is often made by the investigation of toy models, the model organisms of physics, which provide benchmarks for new methodologies. For complex systems, one such model is the adaptive voter model. Despite its simplicity, the model is hard to analyse. Only inaccurate results are obtained from well-established approximation schemes that work well on closely-related models. We use this model to illustrate a new approach that combines a) the use of a heterogeneous moment expansion to approximate the network model by an infinite system of ordinary differential equations, b) generating functions to map the ordinary differential equation system to a two-dimensional partial differential equation, and c) solution of this partial differential equation by the tools of PDE-theory. Beyond the adaptive voter models, the proposed approach establishes a connection between network science and the theory of partial differential equations and is widely applicable to the dynamics of networks with discrete node-states.
Original languageEnglish
Article number093051
Number of pages13
JournalNew Journal of Physics
Volume16
Issue number9
Early online date25 Sep 2014
DOIs
Publication statusPublished - Sep 2014

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