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 neighbours' 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
realisations at a range of model parameter values, on various network
topologies, including random (Erdos-Renyi), small world (Watts-Strogatz) and
(Newman's) highly clustered, community-based networks. An analytical and
probabilistic approach has been developed to account for the observed
behaviour, which explains the results of the numerical calculations
