Gareth Baxter

Research Topics

I am interested in Complex Systems. The patterns of connections and interactions between large numbers of things can give rise to unexpected and complex behaviour, that can't be understood by examining the parts in isolation.

These connections can often be represented as complex networks. I study the structure and function of these network systems, and the effects of interdependence on system functioning and stability.

Many of the systems I am interested in come from fields outside of traditional physics. I'm interested in social collective behaviour, particularly in linguistics, but also applications in areas such as technology, biology.

Language Change

Languages are continually changing. For example, new words are introduced, pronunciations change, meanings of words change, spellings may change. With Alan McKane and Richard Blythe I have been constructing and investigating a model of the process by which language changes occur.

Our model is based on an evolutionary account of language change proposed by Bill Croft. This theory describes language change as an example of generalised evolution as described by David Hull. An essential distinguishing feature of Bill's theory is that the driving force behind changes is the social interactions between speakers:

In other words who says something is more important than any inherent features of what they say.

The first application of this model is an examination of Trudgill's (P. Trudgill New Dialect Formation: The Inevitability of Colonial Englishes, Edinburgh University Press, 2004) explanation of the emergence of New Zealand English from the interaction of the different British and Irish dialects of the European immigrants in the 19th century.

Complex Networks

Networks are a useful way to describe interactions in many real systems, such as social interactions, ecosystems and neurons in the brain. With colleagues in the Complex Networks group in Aveiro, I am studying the structure of networks and novel critical phenomena that occur in networks.

Interdependent Systems

Recently we have been particularly focussing on multilayer and interdependent networked systems. When two or more systems depend on one another in order to function, the whole system can become more fragile. This is important to understand, for example, in infrastructure reliability. Activation of such systems, or recovery after damage, is also important.

Populations, Opinions, Evolution on Networks

Our language change model has analogies with so called neutral evolution in biology. The equations governing the simplest versions of our language model turn out to be virtually identical to the Fisher-Wright diffusion approximation of population genetics. We have extended some of the existing analytic results in this area.

In fact, there are many similarities between models that appear in opinion dynamics, population genetics, biodiversity and language change. All involve the competition between elements (alleles, language variants, opinions, species) that are copied from node to node in a network. If the dynamics are neutral (so no variant has an inherent advantage over the other) many such models can be put on the same footing, and the time taken to reach consensus/fixation on a network can be calculated in the same way.