A model, applicable to a range of innovation diffusion applications with a strong peer-to-peer component, is developed and studied, along with methods for its investigation and analysis. A particular application is to individual households deciding whether to install an energy efficiency measure in their home. The model represents these individuals as nodes on a network, each with a variable representing their current state of adoption of the innovation. The motivation to adopt is composed of three terms, representing personal preference, an average of each individual's network neighbors' states, and a system average, which is a measure of the current social trend. The adoption state of a node changes if a weighted linear combination of these factors exceeds some threshold. Numerical simulations have been carried out, computing the average uptake after a sufficient number of time-steps over many randomizations at all model parameter values, on various network topologies, including random (Erdos-Renyi), small world (Watts-Strogatz), and (Newman) highly clustered, community-based networks. An analytical and probabilistic approach has been developed to account for the observed behavior, which explains the results of the numerical calculations.
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