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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 wellestablished approximation schemes that work well on closelyrelated 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 twodimensional partial diﬀerential equation, and c) solution of this partial diﬀerential equation by the tools of PDEtheory. 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 nodestates.
Original language  English 

Article number  093051 
Number of pages  13 
Journal  New Journal of Physics 
Volume  16 
Issue number  9 
Early online date  25 Sep 2014 
DOIs  
Publication status  Published  Sep 2014 
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Projects
 1 Finished
Profiles

Dr Martin E Homer
 Department of Engineering Mathematics  Associate Professor in Mathematical Modelling
 Applied Nonlinear Mathematics
Person: Academic , Member