This paper presents results from modelling work investigating the effects of social networks on the adoption of energy technologies in the domestic sector. This work concerns ideas on social network interventions which have been successfully applied in other domains but which have seldom been applied to energy policy questions. We employ a dynamical multiparameter network model where households are represented as nodes on a network for which the uptake of technologies is influenced by both personal benefit and social influences. This is applied to demonstrate the usefulness of this type of model in assessing the likely success of different roll-out strategies that a local authority could pursue in promoting the uptake of domestic energy technologies. Local authorities can play a key role in the retrofit of energy-efficiency and low-carbon energy-generation technologies in order to realise carbon reductions and alleviate fuel poverty. Scenarios are modelled for different local authority interventions that target network interactions and uptake threshold effects, and the results provide insights for policy. The potential for the use of this type of modelling in understanding the adoption of energy innovations in the domestic sector and designing local-level interventions is demonstrated.

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 (Erdős-Rényi), 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.

In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction in terms of the component proportions p and the total number of components N . These formulae correctly identify both the percolation limits and also the emergent power law behaviour between the percolation limits and show the interplay between the size of the network and the deviation of the proportion from the critical value of p = 1/2. The results compare excellently with a large number of numerical simulations.

Networks of interactions between competing species are used to model many complex systems, such as in genetics, evolutionary biology or sociology and knowledge of the patterns of activity they can exhibit is important for understanding their behaviour. The emergence of patterns on complex networks with reaction-diffusion dynamics is studied here, where node dynamics interact via diffusion via the network edges. Through the application of a generalisation of dynamical systems analysis this work reveals a fundamental connection between small-scale modes of activity on networks and localised pattern formation seen throughout science, such as solitons, breathers and localised buckling. The connection between solutions with a single and small numbers of activated nodes and the fully developed system-scale patterns are investigated computationally using numerical continuation methods. These techniques are also used to help reveal a much larger portion of of the full number of solutions that exist in the system at different parameter values. The importance of network structure is also highlighted, with a key role being played by nodes with a certain so-called optimal degree, on which the interaction between the reaction kinetics and the network structure organise the behaviour of the system.

We present the results of an experimental investigation of a network of nonlinear coupled oscillators which are coupled in feed-forward mode. By exploiting the nonlinear response of each oscillator near its intrinsic Hopf bifurcation point, we have found remarkable amplification of small signals over a narrow bandwidth with a large dynamic range. The effect is exploited to extract a small amplitude periodic signal from an input time series which is dominated by noise. Specifically, we have used this relatively simple experimental system to measure responses with a bandwidth of approximately 1% of the central frequency, amplifications of approximately 60 dB, and a dynamic range of approximately 80 dB and can extract signals from a time series with a signal to noise ratio of approximately -50 dB.