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• W2012792957 abstract "We derive the generalized master equation for reaction-diffusion on networks from an underlying stochastic process, the continuous time random walk (CTRW). The non-trivial incorporation of the reaction process into the CTRW is achieved by splitting the derivation into two stages. The reactions are treated as birth-death processes and the first stage of the derivation is at the single particle level, taking into account the death process, whilst the second stage considers an ensemble of these particles including the birth process. Using this model we have investigated different types of pattern formation across the vertices on a range of networks. Importantly, the CTRW defines the Laplacian operator on the network in a non emph{ad-hoc} manner and the pattern formation depends on the structure of this Laplacian. Here we focus attention on CTRWs with exponential waiting times for two cases; one in which the rate parameter is constant for all vertices and the other where the rate parameter is proportional to the vertex degree. This results in nonsymmetric and symmetric CTRW Laplacians respectively. In the case of symmetric Laplacians, pattern formation follows from the Turing instability. However in nonsymmetric Laplacians, pattern formation may be possible with or without a Turing instability." @default.
• W2012792957 created "2016-06-24" @default.
• W2012792957 creator A5046766037 @default.
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• W2012792957 date "2013-03-08" @default.
• W2012792957 modified "2023-09-25" @default.
• W2012792957 title "Pattern formation on networks with reactions: A continuous-time random-walk approach" @default.
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• W2012792957 doi "https://doi.org/10.1103/physreve.87.032804" @default.
• W2012792957 hasPublicationYear "2013" @default.
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