Emergent Behaviour in Large Electrical Networks

Many complex systems have emergent behaviour which results from the way in that the components of the system interact, rather than their individual properties. However, it is often unclear as to what this emergent behaviour can be, or inded how large the system should be for such behaviour to arise. In this paper we will address these problems for the specific case of an electrical network comprising a mixture of resistive and reactive elements. Using this model we will show, using some spectral theory, the types of emergent behaviour that we expect and also how large a system we need for this to be observed.