Multi-parameter models of innovation diffusion on complex networks

TL;DR

This paper introduces a multi-parameter network model for innovation diffusion, analyzing how individual decisions are influenced by personal preference, social network, and societal trends, with simulations on various network types and an analytical explanation.

Contribution

It develops a novel multi-parameter model for innovation spread on complex networks, combining numerical simulations with an analytical approach to understand diffusion dynamics.

Findings

Model captures influence of personal, social, and societal factors.

Diffusion patterns vary with network topology.

Analytical methods successfully explain simulation results.

Abstract

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.