PhD research in Boolean networks

Boolean networks are an abstract mathematical model consisting of N connected entities. The entities have just two possible states (0 and 1).

Each entity has a transition rule that specifies the next state as a function of the current states of K other entities, and it is these transition rules that connect the entities together. Boolean networks appear to be a simple system but with a large number of entities they can exhibit complex behaviour. There are applications in physics (e.g. spin glasses), biology (e.g. the evolution of genetic regulatory systems) and business (e.g. marketing and industrial networks).

Research over the past 30 years involving both simulation and mathematical analysis has identifed various properties of Boolean networks. They have attracted attention in recent years as one of the models studied in complexity science. In particular, they can show 3 distinct phases of behaviour - order, chaos and edge of chaos (the phase transition between order and chaos). Much of the research has focussed on finding the conditions in which these different phases occur. A summary of many of the main results is in The Origins of Order by Stuart A. Kauffman (Oxford University Press, 1993).

There are still many aspects of Boolean network behaviour that are not understood. A PhD opportunity exists to investigate these using simulation and mathematical analysis. Good mathematical and computer programming skills are essential. Funding may be available for high calibre applicants.

For further information, please contact Dr Roger Brooks:
phone: +44 (0)1524 593866

If you would like to apply for a PhD, please click here for application information.

Lancaster University Management School is one of only two UK Business Schools to have achieved the top research rating in the last three Research Assessment Exercises. For more information click here